Internal problem ID [7610]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-x y^{2}-3 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 19
dsolve(diff(y(x),x) - x*y(x)^2 - 3*x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {3}{-1+3 \,{\mathrm e}^{-\frac {3 x^{2}}{2}} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.248 (sec). Leaf size: 35
DSolve[y'[x] - x*y[x]^2 - 3*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3}{-1+e^{-\frac {3}{2} \left (x^2+2 c_1\right )}} \\ y(x)\to -3 \\ y(x)\to 0 \\ \end{align*}