29.24.17 problem 679

Internal problem ID [5270]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 24
Problem number : 679
Date solved : Monday, January 27, 2025 at 10:54:26 AM
CAS classification : [_rational]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.295 (sec). Leaf size: 48

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

\[ \text {Solve}\left [-\frac {1}{2} a^2 \log (x-y(x))+\frac {1}{2} a^2 \log (y(x)+x)+\frac {x^2}{2}+\frac {y(x)^2}{2}=c_1,y(x)\right ] \]