Internal problem ID [4047]
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]
\[ \boxed {{y^{\prime }}^{2}+y y^{\prime }-x \left (y+x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) &= \frac {x^{2}}{2}+c_{1} \\ y \left (x \right ) &= 1+{\mathrm e}^{-x} c_{1} -x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.057 (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*}