Internal problem ID [3583]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 29
Problem number: 852.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{2}-\left (x^{2}+1\right ) y^{\prime }+x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(x*diff(y(x),x)^2-(x^2+1)*diff(y(x),x)+x = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1}+\ln \relax (x ) \\ y \relax (x ) = \frac {x^{2}}{2}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 24
DSolve[x (y'[x])^2-(1+x^2)y'[x]+x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2}{2}+c_1 \\ y(x)\to \log (x)+c_1 \\ \end{align*}