Internal problem ID [8440]
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]
\[ \boxed {y^{\prime } x +x y^{2}-\left (2 x^{2}+1\right ) y=x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {x \left (\sqrt {2}+2 \tanh \left (\frac {\left (x^{2}+2 c_{1} \right ) \sqrt {2}}{2}\right )\right ) \sqrt {2}}{2} \]
✓ Solution by Mathematica
Time used: 0.523 (sec). Leaf size: 99
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 \frac {x \left (\left (1+\sqrt {2}\right ) e^{\sqrt {2} x^2}-\left (\sqrt {2}-1\right ) e^{2 \sqrt {2} c_1}\right )}{e^{\sqrt {2} x^2}+e^{2 \sqrt {2} c_1}} y(x)\to \left (1+\sqrt {2}\right ) x y(x)\to x-\sqrt {2} x \end{align*}