Internal problem ID [3602]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 873.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{2}-\left (y x +1\right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve(x*diff(y(x),x)^2-(1+x*y(x))*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1}+\ln \relax (x ) \\ y \relax (x ) = c_{1} {\mathrm e}^{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 20
DSolve[x (y'[x])^2-(1+x y[x])y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^x \\ y(x)\to \log (x)+c_1 \\ \end{align*}