Internal problem ID [7601]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-y^{2}+\left (x^{2}+1\right ) y-2 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 34
dsolve(diff(y(x),x) - y(x)^2 +(x^2 + 1)*y(x) - 2*x=0,y(x), singsol=all)
\[ y \relax (x ) = x^{2}+1+\frac {{\mathrm e}^{\frac {1}{3} x^{3}+x}}{c_{1}-\left (\int {\mathrm e}^{\frac {1}{3} x^{3}+x}d x \right )} \]
✓ Solution by Mathematica
Time used: 0.34 (sec). Leaf size: 58
DSolve[y'[x] - y[x]^2 +(x^2 + 1)*y[x] - 2*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{\frac {x^3}{3}+x}}{-\int _1^xe^{\frac {K[1]^3}{3}+K[1]}dK[1]+c_1}+x^2+1 \\ y(x)\to x^2+1 \\ \end{align*}