Internal problem ID [3418]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 679.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {\left (x \,a^{2}+\left (x^{2}-y^{2}\right ) y\right ) y^{\prime }+x \left (x^{2}-y^{2}\right )-y a^{2}=0} \end {gather*}
✗ 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: 0.322 (sec). Leaf size: 48
DSolve[(a^2 x+y[x] (x^2-y[x]^2))y'[x]+x(x^2-y[x]^2)==a^2 y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {1}{2} a^2 \log (x-y(x))+\frac {1}{2} a^2 \log (y(x)+x)+\frac {x^2}{2}+\frac {y(x)^2}{2}=c_1,y(x)\right ] \]