Internal problem ID [8352]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Riccati]
\[ \boxed {y^{\prime }+y^{2}-2 x^{2} y=-x^{4}+2 x +1} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 35
dsolve(diff(y(x),x) + y(x)^2 - 2*x^2*y(x) + x^4 -2*x-1=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{2} {\mathrm e}^{2 x}-c_{1} x^{2}+{\mathrm e}^{2 x}+c_{1}}{{\mathrm e}^{2 x}-c_{1}} \]
✓ Solution by Mathematica
Time used: 0.137 (sec). Leaf size: 34
DSolve[y'[x] + y[x]^2 - 2*x^2*y[x] + x^4 -2*x-1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2-\frac {2}{1+2 c_1 e^{2 x}}+1 \\ y(x)\to x^2+1 \\ \end{align*}