Internal problem ID [3272]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 528.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {x \left (x +y\right ) y^{\prime }-x^{2}-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 32
dsolve(x*(x+y(x))*diff(y(x),x) = x^2+y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = x \,{\mathrm e}^{-\LambertW \left (\frac {{\mathrm e}^{-\frac {c_{1}}{2}} {\mathrm e}^{-\frac {1}{2}}}{2 \sqrt {x}}\right )-\frac {c_{1}}{2}-\frac {1}{2}-\frac {\ln \relax (x )}{2}}+x \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 30
DSolve[x(x+y[x])y'[x]==x^2+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+2 x \text {ProductLog}\left (\frac {e^{\frac {-1+c_1}{2}}}{2 \sqrt {x}}\right ) \\ \end{align*}