Internal problem ID [3163]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 15
Problem number: 417.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y y^{\prime }+x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(y(x)*diff(y(x),x)+x = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {-x^{2}+c_{1}} \\ y \relax (x ) = -\sqrt {-x^{2}+c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.086 (sec). Leaf size: 39
DSolve[y[x] y'[x]+x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-x^2+2 c_1} \\ y(x)\to \sqrt {-x^2+2 c_1} \\ \end{align*}