Internal problem ID [3626]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 898.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}-2 y y^{\prime } x -x +y \left (1+y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.234 (sec). Leaf size: 22
dsolve(x^2*diff(y(x),x)^2-2*x*diff(y(x),x)*y(x)-x+y(x)*(1+y(x)) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = x \\ y \relax (x ) = c_{1} \sqrt {x}-\frac {c_{1}^{2} x}{4}+x -1 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.112 (sec). Leaf size: 55
DSolve[x^2 (y'[x])^2-2 x y[x] y'[x]-x+y[x](1+y[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+\frac {c_1{}^2 x}{4}-i c_1 \sqrt {x}-1 \\ y(x)\to x+\frac {c_1{}^2 x}{4}+i c_1 \sqrt {x}-1 \\ \end{align*}