06:57
Fundamentals of Differential Equations
Duffing's Equation. In the study of a nonlinear spring with periodic forcing, the following equation arises:
$$
y^{\prime \prime}+k y+r y^{3}=A \cos \omega t
$$
Let $k=r=A=1$ and $\omega=10$. Find the first three nonzero terms in the Taylor polynomial approximations to the solution with initial values $y(0)=0, y^{\prime}(0)=1$.