Internal problem ID [7790]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 210.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y y^{\prime }+x y^{2}-4 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 33
dsolve(y(x)*diff(y(x),x)+x*y(x)^2-4*x=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {{\mathrm e}^{-x^{2}} c_{1}+4} \\ y \relax (x ) = -\sqrt {{\mathrm e}^{-x^{2}} c_{1}+4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.925 (sec). Leaf size: 57
DSolve[y[x]*y'[x]+x*y[x]^2-4*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {4+e^{-x^2+2 c_1}} \\ y(x)\to \sqrt {4+e^{-x^2+2 c_1}} \\ y(x)\to -2 \\ y(x)\to 2 \\ \end{align*}