how to applay y'''+y'=0 , y(0)=y0=0, y'(0)=y01=1, y''(0)=y011=-2 in the following system where fn=y''' i got this error Error using mupadengine/feval (line 157) MuPAD error: Error: Cannot differentiate the equation. [numeric::fsolve] Error in sym

h=0.01
r=0.50091382026531899391478548897399
s=1.5931124176008341060884423751727
dy = diff(y )
d2y = diff(dy )
d3y = diff(d2y )
d3y = -dy
fn(t)=d3y(t)
y0=0
y01=1;
y011=-2;
eq1=-y22-(r - 2)/r*y0+ 2/(r*(r - 1))*yr+ (2*r - 4)/(r - 1)*y1 -(h^3*(3*r^5 - 18*r^4 + 24*r^3 + 24*r^2 - 53*r + 10))/(420*s*(r - s)*(s^2 - 3*s + 2))*fn(s)+ (h^3*(3*r + 21*s - 7*r*s - 21*r^2*s + 7*r^3*s + 7*r^2 + 9*r^3 - 4*r^4 - 5))/(420*r*(r - s)*(r - 1))*fn(r)+ (h^3*(r - 2)*(53*r + 91*s - 77*r*s - 21*r^2*s + 7*r^3*s + 21*r^2 + 5*r^3 - 3*r^4 - 86))/(420*(r - 1)*(s - 1))*fn(y1)+ (h^3*(r - 2)*(24*r + 21*s - 70*r*s + 42*r^2*s - 7*r^3*s - 12*r^3 + 3*r^4 - 5))/(840*r*s)*fn(y0)+ (h^3*(7*s - 4*r + 14*r*s - 7*r^3*s + 2*r^3 + 3*r^4 - 19))/(840*(s - 2))*fn(y22)
eq2=-h*y33 -(r - 3)/r*y0+ 3/(r*(r - 1))*yr+ (r - 4)/(r - 1)*y1+ (h^3*(- 9*r^5 + 54*r^4 - 72*r^3 - 72*r^2 + 117*r + 44))/(840*s*(r - s)*(s^2 - 3*s + 2))*fn(s) -(h^3*(33*r + 84*s - 105*r*s - 105*r^2*s + 105*r^3*s - 21*r^4*s + 33*r^2 + 33*r^3 - 51*r^4 + 12*r^5 + 44))/(840*r*(r - s)*(r^2 - 3*r + 2))*fn(r)+(h^3*(959*r*s - 812*s - 842*r - 105*r^2*s - 105*r^3*s + 21*r^4*s + 33*r^2 + 33*r^3 + 33*r^4 - 9*r^5 + 856))/(840*(r - 1)*(s - 1))*fn(y1) -(h^3*(117*r + 84*s - 469*r*s + 462*r^2*s - 168*r^3*s + 21*r^4*s - 72*r^2 - 72*r^3 + 54*r^4 - 9*r^5 + 44))/(1680*r*s)*fn(y0)-(h^3*(243*r + 252*s - 63*r*s - 42*r^2*s - 42*r^3*s + 21*r^4*s + 12*r^2 + 12*r^3 + 12*r^4 - 9*r^5 - 460))/(1680*(r - 2)*(s - 2))*fn(y22)
eq3=-h^2*y4 + 2/r*y0+ 2/(r*(r - 1))*yr -2/(r - 1)*y1 -(h^3*(r^5 - 6*r^4 + 8*r^3 + 8*r^2 + 8*r - 41))/(140*s*(r - s)*(s^2 - 3*s + 2))*fn(s) -(h^3*(11*r - 35*s - 35*r*s - 35*r^2*s + 35*r^3*s - 7*r^4*s + 11*r^2 + 11*r^3 - 17*r^4 + 4*r^5 + 123))/(420*r*(r - s)*(r^2 - 3*r + 2))*fn(r)+ (h^3*(525*r*s - 539*s - 549*r - 35*r^2*s - 35*r^3*s + 7*r^4*s + 11*r^2 + 11*r^3 + 11*r^4 - 3*r^5 + 662))/(420*(r - 1)*(s - 1))*fn(y1)+ (h^3*(24*r + 35*s + 126*r*s - 154*r^2*s + 56*r^3*s - 7*r^4*s + 24*r^2 + 24*r^3 - 18*r^4 + 3*r^5 - 123))/(840*r*s)*fn(y0) -(h^3*(564*r + 567*s - 294*r*s - 14*r^2*s - 14*r^3*s + 7*r^4*s + 4*r^2 + 4*r^3 + 4*r^4 - 3*r^5 - 1011))/(840*(r - 2)*(s - 2))*fn(y22)
eq4=-h*y111-(r - 1)/r*y0+ 1/(r*(r - 1))*yr+(r - 2)/(r - 1)*y1 -(h^3*(3*r^5 - 18*r^4 + 24*r^3 + 24*r^2 - 53*r + 20))/(840*s*(r - s)*(s^2 - 3*s + 2))*fn(s)+ (h^3*(42*s - 9*r + 7*r*s - 28*r^2*s + 7*r^3*s + 2*r^2 + 13*r^3 - 4*r^4 - 20))/(840*r*(r - s)*(r - 2))*fn(r)+ (h^3*(30*r + 56*s - 63*r*s - 28*r^2*s + 7*r^3*s + 19*r^2 + 8*r^3 - 3*r^4 - 36))/(840*(s - 1))*fn(y1)+ (h^3*(r - 1)*(33*r + 42*s - 105*r*s + 49*r^2*s - 7*r^3*s + 9*r^2 - 15*r^3 + 3*r^4 - 20))/(1680*r*s)*fn(y0) -(h^3*(r - 1)*(9*r + 14*s - 21*r*s - 7*r^2*s + 7*r^3*s + 5*r^2 + r^3 - 3*r^4 - 8))/(1680*(r - 2)*(s - 2))*fn(y22)
eq5=-h^2*y1111+2/r*y0+ 2/(r*(r - 1))*yr-2/(r - 1)*y1 -(h^3*(3*r^5 - 18*r^4 + 24*r^3 + 24*r^2 - 81*r + 38))/(420*s*(r - s)*(s^2 - 3*s + 2))*fn(s) -(h^3*(11*r + 70*s - 35*r*s - 35*r^2*s + 35*r^3*s - 7*r^4*s + 11*r^2 + 11*r^3 - 17*r^4 + 4*r^5 - 38))/(420*r*(r - s)*(r^2 - 3*r + 2))*fn(r)+ (h^3*(245*r*s - 154*s - 164*r - 35*r^2*s - 35*r^3*s + 7*r^4*s + 11*r^2 + 11*r^3 + 11*r^4 - 3*r^5 + 116))/(420*(r - 1)*(s - 1))*fn(y1)+ (h^3*(196*r*s - 70*s - 81*r - 154*r^2*s + 56*r^3*s - 7*r^4*s + 24*r^2 + 24*r^3 - 18*r^4 + 3*r^5 + 38))/(840*r*s)*fn(y0) -(h^3*(56*r*s - 28*s - 31*r - 14*r^2*s - 14*r^3*s + 7*r^4*s + 4*r^2 + 4*r^3 + 4*r^4 - 3*r^5 + 18))/(840*(r - 2)*(s - 2))*fn(y22)
eq6=-h*yr11 +(r - 1)/r*y0+ (2*r - 1)/(r*(r - 1))*yr -r/(r - 1)*y1-(h^3*r*(- 8*r^5 + 45*r^4 - 74*r^3 + 24*r^2 + 24*r - 11))/(840*s*(r - s)*(s^2 - 3*s + 2))*fn(s)+ (h^3*(22*r - 35*s - 70*r*s + 105*r^2*s - 28*r^3*s + 33*r^2 - 68*r^3 + 20*r^4 + 11))/(840*(r - s)*(r - 2))*fn(r) -(h^3*r*(r + 21*s - 14*r*s - 49*r^2*s + 14*r^3*s + 12*r^2 + 23*r^3 - 8*r^4 - 10))/(840*(s - 1))*fn(y1) -(h^3*(r - 1)*(13*r + 35*s - 119*r*s + 77*r^2*s - 14*r^3*s + 37*r^2 - 37*r^3 + 8*r^4 - 11))/(1680*s)*fn(y0)+ (h^3*r*(r - 1)*(r + 7*s - 7*r*s - 21*r^2*s + 14*r^3*s + 5*r^2 + 9*r^3 - 8*r^4 - 3))/(1680*(r - 2)*(s - 2))*fn(y22)
eq7=-h^2*yr111+2/r*y0+ 2/(r*(r - 1))*yr -2/(r - 1)*y1 -(h^3*(- 18*r^5 + 87*r^4 - 116*r^3 + 24*r^2 + 24*r - 11))/(420*s*(r - s)*(s^2 - 3*s + 2))*fn(s) -(h^3*(11*r - 35*s - 35*r*s + 385*r^2*s - 385*r^3*s + 98*r^4*s + 11*r^2 - 269*r^3 + 298*r^4 - 80*r^5 + 11))/(420*r*(r - s)*(r^2 - 3*r + 2))*fn(r)+ (h^3*(11*r + 21*s - 35*r*s - 35*r^2*s + 105*r^3*s - 28*r^4*s + 11*r^2 + 11*r^3 - 59*r^4 + 18*r^5 - 10))/(420*(r - 1)*(s - 1))*fn(y1)+ (h^3*(24*r + 35*s - 154*r*s + 266*r^2*s - 154*r^3*s + 28*r^4*s + 24*r^2 - 116*r^3 + 87*r^4 - 18*r^5 - 11))/(840*r*s)*fn(y0)-(h^3*(4*r + 7*s - 14*r*s - 14*r^2*s + 56*r^3*s - 28*r^4*s + 4*r^2 + 4*r^3 - 31*r^4 + 18*r^5 - 3))/(840*(r - 2)*(s - 2))*fn(y22)
eq8=-ys-((r - s)*(s - 1))/r*y0+ (s*(s - 1))/(r*(r - 1))*yr+ (s*(r - s))/(r - 1)*y1 -(h^3*(3*r^4 + 3*r^3*s - 18*r^3 + 3*r^2*s^2 - 18*r^2*s + 24*r^2 + 3*r*s^3 - 18*r*s^2 + 24*r*s + 24*r - 4*s^4 + 17*s^3 - 11*s^2 - 11*s - 11))/(840*(s - 2))*fn(s)+ (h^3*s*(s - 1)*(- 4*r^4 + 3*r^3*s + 17*r^3 + 3*r^2*s^2 - 18*r^2*s - 11*r^2 + 3*r*s^3 - 18*r*s^2 + 24*r*s - 11*r + 3*s^4 - 18*s^3 + 24*s^2 + 24*s - 11))/(840*r*(r^2 - 3*r + 2))*fn(r) -(h^3*s*(3*r^5 - 7*r^4*s - 11*r^4 + 35*r^3*s - 11*r^3 + 35*r^2*s - 11*r^2 + 7*r*s^4 - 35*r*s^3 - 35*r*s^2 + 10*r - 3*s^5 + 11*s^4 + 11*s^3 + 11*s^2 - 10*s))/(840*(r - 1))*fn(y1) -(h^3*(s - 1)*(- 3*r^5 + 7*r^4*s + 18*r^4 - 56*r^3*s - 24*r^3 + 154*r^2*s - 24*r^2 - 7*r*s^4 + 56*r*s^3 - 154*r*s^2 + 11*r + 3*s^5 - 18*s^4 + 24*s^3 + 24*s^2 - 11*s))/(1680*r)*fn(y0)+ (h^3*s*(s - 1)*(3*r^5 - 7*r^4*s - 4*r^4 + 14*r^3*s - 4*r^3 + 14*r^2*s - 4*r^2 + 7*r*s^4 - 14*r*s^3 - 14*r*s^2 + 3*r - 3*s^5 + 4*s^4 + 4*s^3 + 4*s^2 - 3*s))/(1680*(r - 2)*(s - 2))*fn(y22)
eq9=-h*ys1-(r - 2*s + 1)/r*y0+ (2*s - 1)/(r*(r - 1))*yr+ (r - 2*s)/(r - 1)*y1 -(h^3*(6*r^5*s - 3*r^5 - 36*r^4*s + 18*r^4 + 48*r^3*s - 24*r^3 + 48*r^2*s - 24*r^2 - 42*r*s^5 + 210*r*s^4 - 280*r*s^3 + 48*r*s + 11*r + 28*s^6 - 126*s^5 + 140*s^4 - 22*s))/(840*s*(r - s)*(s^2 - 3*s + 2))*fn(s)+ (h^3*(- 8*r^5*s + 4*r^5 + 14*r^4*s^2 + 27*r^4*s - 17*r^4 - 70*r^3*s^2 + 13*r^3*s + 11*r^3 + 70*r^2*s^2 - 57*r^2*s + 11*r^2 + 70*r*s^2 - 57*r*s + 11*r - 14*s^6 + 84*s^5 - 140*s^4 + 70*s^2 - 22*s))/(840*r*(r - s)*(r^2 - 3*r + 2))*fn(r)+ (h^3*(- 6*r^5*s + 3*r^5 + 14*r^4*s^2 + 15*r^4*s - 11*r^4 - 70*r^3*s^2 + 57*r^3*s - 11*r^3 - 70*r^2*s^2 + 57*r^2*s - 11*r^2 - 28*r*s^5 + 140*r*s^4 - 70*r*s^2 + r*s + 10*r + 14*s^6 - 56*s^5 + 42*s^2 - 20*s))/(840*(r - 1)*(s - 1))*fn(y1) -(h^3*(- 6*r^5*s + 3*r^5 + 14*r^4*s^2 + 29*r^4*s - 18*r^4 - 112*r^3*s^2 + 8*r^3*s + 24*r^3 + 308*r^2*s^2 - 202*r^2*s + 24*r^2 - 28*r*s^5 + 210*r*s^4 - 560*r*s^3 + 308*r*s^2 - 13*r*s - 11*r + 14*s^6 - 84*s^5 + 140*s^4 - 70*s^2 + 22*s))/(1680*r*s)*fn(y0) -(h^3*(- 6*r^5*s + 3*r^5 + 14*r^4*s^2 + r^4*s - 4*r^4 - 28*r^3*s^2 + 22*r^3*s - 4*r^3 - 28*r^2*s^2 + 22*r^2*s - 4*r^2 - 28*r*s^5 + 70*r*s^4 - 28*r*s^2 + r*s + 3*r + 14*s^6 - 28*s^5 + 14*s^2 - 6*s))/(1680*(r - 2)*(s - 2))*fn(y22)
eq10=-h^2*ys11 + 2/r*y0+ 2/(r*(r - 1))*yr -2/(r - 1)*y1 -(h^3*(3*r^5 - 18*r^4 + 24*r^3 + 24*r^2 - 105*r*s^4 + 420*r*s^3 - 420*r*s^2 + 24*r + 84*s^5 - 315*s^4 + 280*s^3 - 11))/(420*s*(r - s)*(s^2 - 3*s + 2))*fn(s) -(h^3*(4*r^5 - 7*r^4*s - 17*r^4 + 35*r^3*s + 11*r^3 - 35*r^2*s + 11*r^2 - 35*r*s + 11*r + 21*s^5 - 105*s^4 + 140*s^3 - 35*s + 11))/(420*r*(r - s)*(r^2 - 3*r + 2))*fn(r)+ (h^3*(- 3*r^5 + 7*r^4*s + 11*r^4 - 35*r^3*s + 11*r^3 - 35*r^2*s + 11*r^2 - 35*r*s^4 + 140*r*s^3 - 35*r*s + 11*r + 21*s^5 - 70*s^4 + 21*s - 10))/(420*(r - 1)*(s - 1))*fn(y1)+ (h^3*(3*r^5 - 7*r^4*s - 18*r^4 + 56*r^3*s + 24*r^3 - 154*r^2*s + 24*r^2 + 35*r*s^4 - 210*r*s^3 + 420*r*s^2 - 154*r*s + 24*r - 21*s^5 + 105*s^4 - 140*s^3 + 35*s - 11))/(840*r*s)*fn(y0) -(h^3*(- 3*r^5 + 7*r^4*s + 4*r^4 - 14*r^3*s + 4*r^3 - 14*r^2*s + 4*r^2 - 35*r*s^4 + 70*r*s^3 - 14*r*s + 4*r + 21*s^5 - 35*s^4 + 7*s - 3))/(840*(r - 2)*(s - 2))*fn(y22)
eq11=-h*y01-(r + 1)/r*y0 -1/(r*(r - 1))*yr+ r/(r - 1)*y1+ (h^3*r*(3*r^4 - 18*r^3 + 24*r^2 + 24*r - 11))/(840*s*(r - s)*(s^2 - 3*s + 2))*fn(s)+ (h^3*(11*r - 35*s - 35*r*s + 35*r^2*s - 7*r^3*s + 11*r^2 - 17*r^3 + 4*r^4 + 11))/(840*(r - s)*(r^2 - 3*r + 2))*fn(r) -(h^3*r*(11*r + 21*s - 35*r*s - 35*r^2*s + 7*r^3*s + 11*r^2 + 11*r^3 - 3*r^4 - 10))/(840*(r - 1)*(s - 1))*fn(y1) -(h^3*(24*r + 35*s - 154*r*s + 56*r^2*s - 7*r^3*s + 24*r^2 - 18*r^3 + 3*r^4 - 11))/(1680*s)*fn(y0)+(h^3*r*(4*r + 7*s - 14*r*s - 14*r^2*s + 7*r^3*s + 4*r^2 + 4*r^3 - 3*r^4 - 3))/(1680*(r - 2)*(s - 2))*fn(y22)
eq12=-h^2*y011+2/r*y0+ 2/(r*(r - 1))*yr -2/(r - 1)*y1 -(h^3*(3*r^5 - 18*r^4 + 24*r^3 + 24*r^2 + 24*r - 11))/(420*s*(r - s)*(s^2 - 3*s + 2))*fn(s) -(h^3*(11*r - 35*s - 35*r*s - 35*r^2*s + 35*r^3*s - 7*r^4*s + 11*r^2 + 11*r^3 - 17*r^4 + 4*r^5 + 11))/(420*r*(r - s)*(r^2 - 3*r + 2))*fn(r)+ (h^3*(11*r + 21*s - 35*r*s - 35*r^2*s - 35*r^3*s + 7*r^4*s + 11*r^2 + 11*r^3 + 11*r^4 - 3*r^5 - 10))/(420*(r - 1)*(s - 1))*fn(y1)+ (h^3*(24*r + 35*s - 154*r*s - 154*r^2*s + 56*r^3*s - 7*r^4*s + 24*r^2 + 24*r^3 - 18*r^4 + 3*r^5 - 11))/(840*r*s)*fn(y0) -(h^3*(4*r + 7*s - 14*r*s - 14*r^2*s - 14*r^3*s + 7*r^4*s + 4*r^2 + 4*r^3 + 4*r^4 - 3*r^5 - 3))/(840*(r - 2)*(s - 2))*fn(y22)

[y1,y111,y1111,y22,y4,y33,yr,yr11,yr111,ys,ys1,ys11]=vpasolve([eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9,eq10,eq11,eq12])

Answer 1

[Walter Roberson]

Change

syms y

to

syms y(t)

[Walter Roberson]

Your revised code is missing the "syms" completely. And doesn't define y1 or y22 or some other variables.

[Walter Roberson]

syms y(t) y1 y111 y1111 y22 y33 y4 yr yr11 yr111 ys ys1 ys11

the vpasolve() will fail, though. vpasolve() cannot handle differential equations. dsolve() cannot handle those particular differential equations.

[sadeem alqarni]

When I try the (solve), wait for two hours for the results not appear

[Walter Roberson]

Maple cannot handle those equations either; it gets confused by the evaluation of the derivative at several symbolic locations, y0, y1, y22 . If I replace the invocation of the derivative at those locations with symbolic variables (e.g., temporarily calling them constants), then Maple gives up immediately.

It is plausible that it would be possible to get further if some of y1 y111 y1111 y22 y33 y4 yr yr11 yr111 ys ys1 ys11 had been given numeric values.