Nonlinear Differential Equation Solving

Hello everyone.

I have a second order non-linear homogenous differential equation I want to solve.

Equation basicly is : A*y'' - B*y + C = D*cos(y)

How can i solve this? I am trying to acquire a solution in the form of y = ....

Note = y'' is second order derivative of y

Answer 1

[Sam Chak]

Hi @Nuri Efe TATLI

The analytical solution probably does not exist.

syms y(t) A B C D
eqn = A*diff(y,t,2) - B*y + C == D*cos(y);
ySol(t) = dsolve(eqn)

Try ode45 instead if the parameters {A, B, C, D} are known. See some examples here:

https://www.mathworks.com/help/matlab/ref/ode45.html

[Nuri Efe TATLI]

Thanks for the swift answer @Sam Chak

Could i possibly get an analytical solution if i linearize the equation and solve it for y ?

If i can what would be the way to do this ?

Thanks in advance !

[Sam Chak]

Yes @Nuri Efe TATLI. If cos(y) is linearized at y = 0, where , then the analytical solution exists.

syms y(t) A B C D
eqn = A*diff(y,t,2) - B*y + C == D;
ySol(t) = dsolve(eqn)

ySol(t) =