29.33.14 problem 976

Internal problem ID [5553]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 33
Problem number : 976
Date solved : Monday, January 27, 2025 at 11:46:23 AM
CAS classification : [_separable]

\begin{align*} y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+x^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.074 (sec). Leaf size: 31

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

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

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 39

DSolve[y[x]^2 (D[y[x],x])^2+2 x y[x] D[y[x],x]+x^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {-x^2+2 c_1} \\ y(x)\to \sqrt {-x^2+2 c_1} \\ \end{align*}