Internal problem ID [3302]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 558.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {a x y y^{\prime }-x^{2}-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 80
dsolve(a*x*y(x)*diff(y(x),x) = x^2+y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {\left (a -1\right ) \left (x^{\frac {2}{a}} c_{1} a -x^{\frac {2}{a}} c_{1}+x^{2}\right )}}{a -1} \\ y \relax (x ) = -\frac {\sqrt {\left (a -1\right ) \left (x^{\frac {2}{a}} c_{1} a -x^{\frac {2}{a}} c_{1}+x^{2}\right )}}{a -1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.003 (sec). Leaf size: 68
DSolve[a x y[x] y'[x]==x^2+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {x^2+(a-1) c_1 x^{2/a}}}{\sqrt {a-1}} \\ y(x)\to \frac {\sqrt {x^2+(a-1) c_1 x^{2/a}}}{\sqrt {a-1}} \\ \end{align*}