Internal problem ID [3541]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 28
Problem number: 810.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+\left (x +y\right ) y^{\prime }+y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x)^2+(x+y(x))*diff(y(x),x)+x*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {x^{2}}{2}+c_{1} \\ y \relax (x ) = {\mathrm e}^{-x} c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 32
DSolve[(y'[x])^2+(x+y[x])y'[x]+x y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-x} \\ y(x)\to -\frac {x^2}{2}+c_1 \\ y(x)\to 0 \\ \end{align*}