dsolve() function yielding errors

Have been trying to solve the following equation for some time, but when I run the same it yields some errors which I'm unable to understand.

inits='x(0)=0,r(0)=0,s(0)=0,q(0)=0';
eqn1='40000*x-20000*s-20000*q+500*Dx-250*Ds-250*Dq+750*D2x=0';
eqn2='90000*r+30000*s-30000q+1125*Dr+375*Ds-375*Dq+1000*D2r=0';
eqn3='-20000*x+30000*r+220000*s-250*Dx+375*Dr+250*Ds+35*D2s=2000000';
eqn4='-20000*x+30000*r+220000*q-250*Dx+375*Dr+250*Dq+35*D2q=2000000';
[x,r,s,q]=dsolve('eqn1','eqn2','eqn3','eqn4',inits);

This is yielding the following error

Error using symengine (line 58)
Could not extract differential variables to solve for. Use 'solve'
or 'vpasolve' to compute the solutions of non-differential
equations.

Error in mupadengine/feval (line 155)
                  symengine('error',S(8:find(S=='[',1)-2));

Error in dsolve>mupadDsolve (line 325)
T = feval(symengine,'symobj::dsolve',sys,x,options);

Error in dsolve (line 186)
sol = mupadDsolve(args, options);

Error in Pitch_equation_of_motion_solve (line 6)
[x,r,s,q]=dsolve('eqn1','eqn2','eqn3','eqn4',inits);

Answer 1

[Torsten]

1. Define x(t),r(t),s(t),q(t) as symbolic

2. Use "==" instead of "=" in the definition of the equations

3. Use diff(x), diff(r), diff(s), diff(q) instead of Dx, Dr, Ds, Dq.

Best wishes

Torsten.

[Nishanth]

Thank you for your answer. As you suggested, I made the necessary changes & ran the script. But this too isn't working.

syms x(t) r(t) s(t) q(t) inits='x(0)=0,r(0)=0,s(0)=0,q(0)=0'; eqn1='40000*x-20000*s-20000*q+500*diff(x)-250*diff(s)-250*diff(q)+750*diff(diff(x))=0'; eqn2='90000*r+30000*s-30000q+1125*diff(r)+375*diff(s)-375*diff(q)+1000*diff(diff(r))=0'; eqn3='-20000*x+30000*r+220000*s-250*diff(x)+375*diff(r)+250*diff(s)+35*diff(diff(s))=2000000'; eqn4='-20000*x+30000*r+220000*q-250*diff(x)+375*diff(r)+250*diff(q)+35*diff(diff(q))=2000000'; [x,r,s,q]=dsolve('eqn1','eqn2','eqn3','eqn4',inits);

Is there something that I'm doing differently? Your feedback would be really helpful.

It is yielding the following error:

Error using symengine (line 58) Could not extract differential variables to solve for. Use 'solve' or 'vpasolve' to compute the solutions of non-differential equations.

Error in mupadengine/feval (line 155) symengine('error',S(8:find(S=='[',1)-2));

Error in dsolve>mupadDsolve (line 325) T = feval(symengine,'symobj::dsolve',sys,x,options);

Error in dsolve (line 186) sol = mupadDsolve(args, options);

[Torsten]

You still use "=" instead of "==" in the definition of the eqn's. This is wrong.

Replace

[x,r,s,q]=dsolve('eqn1','eqn2','eqn3','eqn4',inits);

by

[x,r,s,q]=dsolve(eqn1,eqn2,eqn3,eqn4,inits);

If your code still does not work, insert the eqn's directly in the call to dsolve:

[x,r,s,q]=dsolve(40000*x-20000*s-20000*q+500*diff(x)-250*diff(s)-250*diff(q)+750*diff(diff(x))==0,90000*r+30000*s-30000q+1125*diff(r)+375*diff(s)-375*diff(q)+1000*diff(diff(r))==0,-20000*x+30000*r+220000*s-250*diff(x)+375*diff(r)+250*diff(s)+35*diff(diff(s))==2000000,-20000*x+30000*r+220000*q-250*diff(x)+375*diff(r)+250*diff(q)+35*diff(diff(q))==2000000,x(0)==0,r(0)==0,s(0)==0,q(0)==0);

Best wishes

Torsten

[Nishanth]

*Hello Mr.Tosten, Thank you for helping me out. But, even after trying out your suggestion, the problem seems to persist.

For the below input

syms x(t) r(t) s(t) q(t)

[x,r,s,q]=dsolve(40000*x-20000*s-20000*q+500*diff(x)-250*diff(s)-250*diff(q)+750*diff(diff(x))==0,90000*r+30000*s-30000q+1125*diff(r)+375*diff(s)-375*diff(q)+1000*diff(diff(r))==0,-20000*x+30000*r+220000*s-250*diff(x)+375*diff(r)+250*diff(s)+35*diff(diff(s))==2000000,-20000*x+30000*r+220000*q-250*diff(x)+375*diff(r)+250*diff(q)+35*diff(diff(q))==2000000,x(0)==0,r(0)==0,s(0)==0,q(0)==0);

The function is yielding the following error.

Error: Unexpected MATLAB expression.

So, I tried out the following input:(With quotes for equations)

syms x(t) r(t) s(t) q(t) >> [x,r,s,q]=dsolve('40000*x-20000*s-20000*q+500*diff(x)-250*diff(s)-250*diff(q)+750*diff(diff(x))==0','90000*r+30000*s-30000q+1125*diff(r)+375*diff(s)-375*diff(q)+1000*diff(diff(r))==0','-20000*x+30000*r+220000*s-250*diff(x)+375*diff(r)+250*diff(s)+35*diff(diff(s))==2000000,-20000*x+30000*r+220000*q-250*diff(x)+375*diff(r)+250*diff(q)+35*diff(diff(q))==2000000',x(0)==0,r(0)==0,s(0)==0,q(0)==0);

Which resulted in the following error:

Error using sym>convertExpression (line 2246) Conversion to 'sym' returned the MuPAD error: Error: Unexpected 'identifier'. [line 1, col 112]

Error in sym>convertChar (line 2157) s = convertExpression(x);

Error in sym>convertCharWithOption (line 2140) s = convertChar(x);

Error in sym>tomupad (line 1871) S = convertCharWithOption(x,a);

Error in sym (line 104) S.s = tomupad(x,'');

Error in dsolve>mupadDsolve (line 324) sys = [sys_sym sym(sys_str)];*

Hope, You can help me out..

With Regards

Nishanth

[Torsten]

I read in the examples for dsolve. It's necessary to use diff(r,2) instead of diff(diff(r)) (same for the other unknown functions).

By the way: You have 4 second order equations ; so you will need 8 boundary conditions instead of 4 to fix the solution.

Best wishes

Torsten.

[Nishanth]

As you suggested, I tried out diff(r,2) & also added the the needed boundary conditions.

syms x(t) r(t) s(t) q(t) [x,r,s,q]=dsolve('40000*x-20000*s-20000*q+500*diff(x)-250*diff(s)-250*diff(q)+750*diff(x,2)==0', '90000*r+30000*s-30000q+1125*diff(r)+375*diff(s)-375*diff(q)+1000*diff(r,2)==0', '-20000*x+30000*r+220000*s-250*diff(x)+375*diff(r)+250*diff(s)+35*diff(s,2)==2000000', '-20000*x+30000*r+220000*q-250*diff(x)+375*diff(r)+250*diff(q)+35*diff(q,2)==2000000', 'diff(x(0))==0','diff(r(0))==0','diff(s(0))==0','diff(q(0)==0)','x(0)==0','r(0)==0','s(0)==0','q(0)==0');

Still no output. It is yielding the same errors as earlier. Would like to hear from you, on this. Please, need the community's help to resolve this.

[Torsten]

Why do you still use ' ' to frame your equations ? They are wrong.

Best wishes Torsten.

[Torsten]

So, does this call to dsolve work ? If not, what is the error message ?

syms x(t) r(t) s(t) q(t)

[x,r,s,q]=dsolve(40000*x-20000*s-20000*q+500*diff(x)-250*diff(s)-250*diff(q)+750*diff(x,2)==0,90000*r+30000*s-30000q+1125*diff(r)+375*diff(s)-375*diff(q)+1000*diff(r,2)==0,-20000*x+30000*r+220000*s-250*diff(x)+375*diff(r)+250*diff(s)+35*diff(s,2)==2000000,-20000*x+30000*r+220000*q-250*diff(x)+375*diff(r)+250*diff(q)+35*diff(q,2)==2000000, Dx(0)==0,Dr(0)==0,Ds(0)==0,Dq(0)==0,x(0)==0,r(0)==0,s(0)==0,q(0)==0);

Best wishes

Torsten.

[Nishanth]

I used '' to frame my equations, because that is how the function defines me to do it.

And Mr.Torsten the one you suggested above, returns the following message

Error: Unexpected MATLAB expression.

[Torsten]

Last attempt:

syms x(t) r(t) s(t) q(t)
Dx=diff(x);
Dr=diff(r);
Ds=diff(s);
Dq=diff(q);
D2x=diff(x,2);
D2r=diff(r,2);
D2s=diff(s,2);
D2q=diff(q,2);
[X,R,S,Q]=dsolve(40000*x-20000*s-20000*q+500*Dx-250*Ds-250*Dq+750*D2x==0,90000*r+30000*s-30000q+1125*Dr+375*Ds-375*Dq+1000*D2r==0,-20000*x+30000*r+220000*s-250*Dx+375*Dr+250*Ds+35*D2s==2000000,-20000*x+30000*r+220000*q-250*Dx+375*Dr+250*Dq+35*D2q==2000000,Dx(0)==0,Dr(0)==0,Ds(0)==0,Dq(0)==0,x(0)==0,r(0)==0,s(0)==0,q(0)==0);

Best wishes

Torsten.