Internal problem ID [7684]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Riccati]
Solve \begin {gather*} \boxed {x y^{\prime }+x y^{2}-\left (2 x^{2}+1\right ) y-x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 29
dsolve(x*diff(y(x),x) + x*y(x)^2 - (2*x^2+1)*y(x) - x^3=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x \left (\sqrt {2}+2 \tanh \left (\frac {\left (x^{2}+2 c_{1}\right ) \sqrt {2}}{2}\right )\right ) \sqrt {2}}{2} \]
✓ Solution by Mathematica
Time used: 0.54 (sec). Leaf size: 56
DSolve[x*y'[x] + x*y[x]^2 - (2*x^2+1)*y[x] - x^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+\sqrt {2} x \tanh \left (\frac {x^2-2 c_1}{\sqrt {2}}\right ) \\ y(x)\to \left (1+\sqrt {2}\right ) x \\ y(x)\to x-\sqrt {2} x \\ \end{align*}