Internal problem ID [8022]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 442.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}+\left (x^{2} y-2 y x +x^{3}\right ) y^{\prime }+\left (y^{2}-x^{2} y\right ) \left (1-x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 21
dsolve(x^2*diff(y(x),x)^2+(x^2*y(x)-2*x*y(x)+x^3)*diff(y(x),x)+(y(x)^2-x^2*y(x))*(1-x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (c_{1}-x \right ) x \\ y \relax (x ) = c_{1} x \,{\mathrm e}^{-x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.054 (sec). Leaf size: 26
DSolve[(1 - x)*(-(x^2*y[x]) + y[x]^2) + (x^3 - 2*x*y[x] + x^2*y[x])*y'[x] + x^2*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-x} x \\ y(x)\to x (-x+c_1) \\ \end{align*}