Internal problem ID [3203]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 16
Problem number: 457.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]], [_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {\left (x^{2}-y\right ) y^{\prime }+x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 23
dsolve((x^2-y(x))*diff(y(x),x)+x = 0,y(x), singsol=all)
\[ y \relax (x ) = x^{2}+\frac {\LambertW \left (4 c_{1} {\mathrm e}^{-2 x^{2}-1}\right )}{2}+\frac {1}{2} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 29
DSolve[(x^2-y[x])y'[x]+x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2+\frac {1}{2} \left (1+\text {ProductLog}\left (-e^{-2 x^2-1+c_1}\right )\right ) \\ \end{align*}