Internal problem ID [2800]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 45.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-2 x +y \left (x^{2}+1\right )-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x) = 2*x-(x^2+1)*y(x)+y(x)^2,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: 0.348 (sec). Leaf size: 58
DSolve[y'[x]==2 x-(1+x^2)y[x]+y[x]^2,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*}