Internal problem ID [3678]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 32
Problem number: 952.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y \left (y^{\prime }\right )^{2}+\left (-y^{2}+x \right ) y^{\prime }-y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 34
dsolve(y(x)*diff(y(x),x)^2+(x-y(x)^2)*diff(y(x),x)-x*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {-x^{2}+c_{1}} \\ y \relax (x ) = -\sqrt {-x^{2}+c_{1}} \\ y \relax (x ) = c_{1} {\mathrm e}^{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.092 (sec). Leaf size: 54
DSolve[y[x] (y'[x])^2+(x-y[x]^2)y'[x]-x y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^x \\ y(x)\to -\sqrt {-x^2+2 c_1} \\ y(x)\to \sqrt {-x^2+2 c_1} \\ y(x)\to 0 \\ \end{align*}