Internal problem ID [8365]
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]
\[ \boxed {y^{\prime }+x y^{2}-y x^{3}=2 x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 51
dsolve(diff(y(x),x) + x*y(x)^2 -x^3*y(x) - 2*x=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sqrt {\pi }\, \operatorname {erf}\left (\frac {x^{2}}{2}\right ) c_{1} x^{2}+\sqrt {\pi }\, x^{2}+2 \,{\mathrm e}^{-\frac {x^{4}}{4}} c_{1}}{\sqrt {\pi }\, \left (\operatorname {erf}\left (\frac {x^{2}}{2}\right ) c_{1} +1\right )} \]
✓ Solution by Mathematica
Time used: 0.317 (sec). Leaf size: 70
DSolve[y'[x] + x*y[x]^2 -x^3*y[x] - 2*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {\pi } x^2 \text {erf}\left (\frac {x^2}{2}\right )+2 e^{-\frac {x^4}{4}}+2 c_1 x^2}{\sqrt {\pi } \text {erf}\left (\frac {x^2}{2}\right )+2 c_1} \\ y(x)\to x^2 \\ \end{align*}