29.26.24 problem 760

Internal problem ID [5345]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 760
Date solved : Monday, January 27, 2025 at 11:15:59 AM
CAS classification : [_separable]

\begin{align*} {y^{\prime }}^{2}&=x^{2} y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 23

dsolve(diff(y(x),x)^2 = x^2*y(x)^2,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= {\mathrm e}^{\frac {x^{2}}{2}} c_{1} \\ y \left (x \right ) &= {\mathrm e}^{-\frac {x^{2}}{2}} c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 38

DSolve[(D[y[x],x])^2==x^2*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{-\frac {x^2}{2}} \\ y(x)\to c_1 e^{\frac {x^2}{2}} \\ y(x)\to 0 \\ \end{align*}