65.5.6 problem 10.3 (i)

Internal problem ID [13745]
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)
Date solved : Tuesday, January 28, 2025 at 06:01:06 AM
CAS classification : [_separable]

\begin{align*} V^{\prime }\left (x \right )+2 y^{\prime } y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 25

dsolve(diff(V(x),x)+2*y(x)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \sqrt {-V+c_{1}} \\ y &= -\sqrt {-V+c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.079 (sec). Leaf size: 68

DSolve[D[ V[x],x]+2*y[x]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {2} \sqrt {\int _1^x-\frac {1}{2} V''(K[1])dK[1]+c_1} \\ y(x)\to \sqrt {2} \sqrt {\int _1^x-\frac {1}{2} V''(K[1])dK[1]+c_1} \\ \end{align*}