Internal problem ID [3539]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 28
Problem number: 808.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+y y^{\prime }-x \left (x +y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(diff(y(x),x)^2+y(x)*diff(y(x),x) = x*(x+y(x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x^{2}}{2}+c_{1} \\ y \relax (x ) = -x +1+{\mathrm e}^{-x} c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.054 (sec). Leaf size: 32
DSolve[(y'[x])^2+y[x] y'[x]==x(x+y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2}{2}+c_1 \\ y(x)\to -x+c_1 e^{-x}+1 \\ \end{align*}