Internal problem ID [2796]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 41.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }+1-x -y \left (x +y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 47
dsolve(diff(y(x),x)+1-x = (x+y(x))*y(x),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: 0.167 (sec). Leaf size: 54
DSolve[y'[x]+1-x==(x+y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1+\frac {2 e^{\frac {1}{2} (x-2)^2}}{-\sqrt {2 \pi } \text {Erfi}\left (\frac {x-2}{\sqrt {2}}\right )+2 e^2 c_1} \\ y(x)\to -1 \\ \end{align*}