Internal problem ID [7599]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-y^{2}-y x -x +1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 47
dsolve(diff(y(x),x) - y(x)^2 - x*y(x) - x + 1=0,y(x), singsol=all)
\[ y \relax (x ) = -1+\frac {{\mathrm e}^{\frac {1}{2} x^{2}-2 x}}{c_{1}+\frac {i \sqrt {\pi }\, {\mathrm e}^{-2} \sqrt {2}\, \erf \left (\frac {i \sqrt {2}\, x}{2}-i \sqrt {2}\right )}{2}} \]
✓ Solution by Mathematica
Time used: 0.182 (sec). Leaf size: 54
DSolve[y'[x]- y[x]^2 - x*y[x] - x + 1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1+\frac {2 e^{\frac {1}{2} (x-2)^2}}{-\sqrt {2 \pi } \operatorname {Erfi}\left (\frac {x-2}{\sqrt {2}}\right )+2 e^2 c_1} \\ y(x)\to -1 \\ \end{align*}