how to solve this second order deferential equation with constants symbols

Hi, i am struggling to solve this equation. please help me to code this on matlab or any other method to solve this . thanks

Answer 1

[Walter Roberson]

syms theta(t) theta0 dtheta0
Dtheta = diff(theta); D2theta = diff(Dtheta);
dsolve([I*D2theta == K1*Dtheta - K2*Dtheta^2, theta(0)==theta0,Dtheta(0)==dtheta0])

ans =
(I*log(-(exp(-(K1*K2*(C34 - t/K2))/I) - (I*log(-exp(-(K2*theta0)/I)/(K2*dtheta0)))/(K1*K2))/K1))/K2

However, this answer does not seem to be correct: it involves the arbitrary constant C34 without good reason.

[Dan Mathotaarchchi]

thank you . will there be any method to define c34? however when i try to solve it this appears. ''??? Error using ==> syms at 61'' in this problem , K1,K2,I are positive. and t and theta also positive. t vs theta to be graphed too. highly appreciated your answer many thanks

[Torsten]

http://www.wolframalpha.com/input/?i=c*y''(t)+-+d*y'(t)+-+e*y'(t)%5E2+%3D+0

Best wishes

Torsten.

[Walter Roberson]

Yes... the problem is that MATLAB is getting the wrong solution.

[Torsten]

I suggest using "Copy and Paste" :-)

Best wishes

Torsten.

[Walter Roberson]

By the way, you get the same incorrect solution for

dsolve('I_*D2y = K1*Dy - K2*(Dy)^2', 'y(0)=y0', 'Dy(0)=dy0')

Note that I had to substitute I_ for I: in this particular context, I by itself would be interpreted as sqrt(-1)

[Walter Roberson]

I just submitted a bug report about this.

[Walter Roberson]

I just submitted a bug report about this.

[Dan Mathotaarchchi]

thank you Torson but the link seems not working

[Dan Mathotaarchchi]

thank you Walter