Internal problem ID [8546]
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]
\[ \boxed {y y^{\prime }+x y^{2}=4 x} \]
✓ Solution by Maple
Time used: 0.016 (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 \left (x \right ) &= \sqrt {c_{1} {\mathrm e}^{-x^{2}}+4} \\ y \left (x \right ) &= -\sqrt {c_{1} {\mathrm e}^{-x^{2}}+4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.932 (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*}