Internal problem ID [3552]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 28
Problem number: 821.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-\left (2 y x +1\right ) y^{\prime }+2 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 16
dsolve(diff(y(x),x)^2-(1+2*x*y(x))*diff(y(x),x)+2*x*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1} {\mathrm e}^{x^{2}} \\ y \relax (x ) = c_{1}+x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 21
DSolve[(y'[x])^2-(1+2 x y[x])y'[x]+2 x y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{x^2} \\ y(x)\to x+c_1 \\ \end{align*}