Internal problem ID [7609]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }+x y^{2}-y x^{3}-2 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 67
dsolve(diff(y(x),x) + x*y(x)^2 -x^3*y(x) - 2*x=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {2 c_{1} {\mathrm e}^{-\frac {x^{4}}{4}}}{\sqrt {\pi }\, \left (\erf \left (\frac {x^{2}}{2}\right ) c_{1}+1\right )}+\frac {\erf \left (\frac {x^{2}}{2}\right ) \sqrt {\pi }\, c_{1} x^{2}+\sqrt {\pi }\, x^{2}}{\sqrt {\pi }\, \left (\erf \left (\frac {x^{2}}{2}\right ) c_{1}+1\right )} \]
✓ Solution by Mathematica
Time used: 0.444 (sec). Leaf size: 48
DSolve[y'[x] + x*y[x]^2 -x^3*y[x] - 2*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2+\frac {2 e^{-\frac {x^4}{4}}}{\sqrt {\pi } \text {Erf}\left (\frac {x^2}{2}\right )+2 c_1} \\ y(x)\to x^2 \\ \end{align*}