Solve sine and exponential nonlinear differential equation?

127 Views Asked by At

Is it possible to solve this kind of differential equation with forward Euler?

$$\ddot y^2 + sin(\ddot y ) + \dot y + y = u$$

I haven't even write this ODE on the first order form. If I would do that, I would say $\dot y = x_2$ and $y = x_1$. Then the ODE would be:

$$x_2 = \dot x_1$$ $$\dot x_2^2 + sin(\dot x_2 ) + x_2 + x_1 = u$$

Then I move all the derivatives to the LHP and non-derivatives to RHP.

$$\dot x_1 = x_2 $$ $$\dot x_2^2 + sin(\dot x_2 )= u - x_2 - x_1 $$

But how about these: $\dot x_2^2 + sin(\dot x_2 )$ ? My goal is to find $\dot x_2$.