Internal problem ID [3810]
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]
\[ \boxed {a x y y^{\prime }-y^{2}=x^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 64
dsolve(a*x*y(x)*diff(y(x),x) = x^2+y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\sqrt {\left (c_{1} \left (a -1\right ) x^{\frac {2}{a}}+x^{2}\right ) \left (a -1\right )}}{a -1} \\ y \left (x \right ) &= -\frac {\sqrt {\left (c_{1} \left (a -1\right ) x^{\frac {2}{a}}+x^{2}\right ) \left (a -1\right )}}{a -1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.315 (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*}