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Nonlinear Differential Equation Solving

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Nuri Efe TATLI
Nuri Efe TATLI 2022-6-14
评论： Sam Chak 2022-6-14
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

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Sam Chak
Sam Chak 2022-6-14
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
  2 个评论
Nuri Efe TATLI
Nuri Efe TATLI 2022-6-14
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
Sam Chak 2022-6-14
Ran in:
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) = 

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