Home /
Expert Answers /
Other Math /
the-van-der-pol-equation-has-the-form-d-2y-dt-2-1-y2-dy-dt-y-0-given-the-initial-co-pa914
(Solved): The Van der Pol equation has the form: d^2y/dt^2 - (1-y2)*dy/dt + y = 0 Given the initial co ...
The Van der Pol equation has the form:
d^2y/dt^2 - (1-y2)*dy/dt + y = 0
Given the initial conditions, y(0) - y'(0) = 1, solve this equation from t = 0 to 2 using Euler's method with a step size of 0.25.
Hint: use the transformation x = dy/dt to express the 2nd order ODE into a system of two 1st order ODEs.
![3. The Van der Pol equation has the form:
\[
\frac{d^{2} y}{d t^{2}}-\left(1-y^{2}\right) \frac{d y}{d t}+y=0
\]
Given the in](https://media.cheggcdn.com/media/57a/57a9f297-f01b-47bb-ba21-37927b4acef1/php7REEGm)
3. The Van der Pol equation has the form: Given the initial conditions, , solve this equation from to 2 using Euler's method with a step size of 0.25 . Hint: use the transformation to express the order into a system of two order ODEs.
Expert Answer
To solve the given Van der pol's equation using Euler's method, we must rewrite it as a system of two first order differential equation. Let,.X=dy/dt &. dX/dt = (1-y^2)X - yLet,. X=dy/dt &. dX/dt = (1-y^2)X - yLet,. X=dy/dt &. dX/dt = (1-y^2)X - yVan der pol equation is the mathematical model of second order ordinary differential equation with cubic nonlinearity.