Internal problem ID [3700]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 975.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{2} \left (y^{\prime }\right )^{2}-\left (x +1\right ) y y^{\prime }+x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 45
dsolve(y(x)^2*diff(y(x),x)^2-(1+x)*y(x)*diff(y(x),x)+x = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {2 x +c_{1}} \\ y \relax (x ) = -\sqrt {2 x +c_{1}} \\ y \relax (x ) = \sqrt {x^{2}+c_{1}} \\ y \relax (x ) = -\sqrt {x^{2}+c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.074 (sec). Leaf size: 72
DSolve[y[x]^2 (y'[x])^2-(1+x)y[x] y'[x]+x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2} \sqrt {x+c_1} \\ y(x)\to \sqrt {2} \sqrt {x+c_1} \\ y(x)\to -\sqrt {x^2+2 c_1} \\ y(x)\to \sqrt {x^2+2 c_1} \\ \end{align*}