How to write down first order system of equations equivalent to the differential equation $$\frac{d^3y}{dx^3}=\frac{d^2y}{dx^2}-x^2\Big(\frac{dy}{dx}\Big)^2.$$
How to write first order system of equations equivalent to certain ODE
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ordinary-differential-equations
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0The first thing you can do is to introduce a new function: $$u(x)=dy/dx$$, because there are only derivatives in your equation. – 2017-01-22
1 Answers
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we have the ODE :$\frac{d^3y}{dx^3}=\frac{d^2y}{dx^2}-x^2\Big(\frac{dy}{dx}\Big)^2$which can be written as
\begin{align} y_1&=y'\\ y_2&=y_1'\\ y_2'&=y_2-x^2y_1^2 \end{align}