Internal problem ID [11673]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number: 40.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }+y^{2}-y x=1} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 53
dsolve(diff(y(x),x)=-y(x)^2+x*y(x)+1,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {x \sqrt {2}}{2}\right ) x +2 c_{1} x +2 \,{\mathrm e}^{-\frac {x^{2}}{2}}}{\sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {x \sqrt {2}}{2}\right )+2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.154 (sec). Leaf size: 45
DSolve[y'[x]==-y[x]^2+x*y[x]+1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+\frac {e^{-\frac {x^2}{2}}}{\sqrt {\frac {\pi }{2}} \text {erf}\left (\frac {x}{\sqrt {2}}\right )+c_1} \\ y(x)\to x \\ \end{align*}