Internal problem ID [11689]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 10, Two tricks for nonlinear equations. Exercises page 97
Problem number: 10.3 (i).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {2 y y^{\prime }=-V^{\prime }\left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(diff(V(x),x)+2*y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {-V \left (x \right )+c_{1}} y \left (x \right ) = -\sqrt {-V \left (x \right )+c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.126 (sec). Leaf size: 37
DSolve[V'[x]+2*y[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-V(x)+2 c_1} y(x)\to \sqrt {-V(x)+2 c_1} \end{align*}