Internal problem ID [11672]
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: 39.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-\left (1-x \right ) y^{2}-\left (2 x -1\right ) y=-x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x)=(1-x)*y(x)^2+(2*x-1)*y(x)-x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (2 x -2\right ) {\mathrm e}^{x}-c_{1}}{\left (2 x -4\right ) {\mathrm e}^{x}-c_{1}} \]
✓ Solution by Mathematica
Time used: 0.197 (sec). Leaf size: 28
DSolve[y'[x]==(1-x)*y[x]^2+(2*x-1)*y[x]-x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1+\frac {e^x}{e^x (x-2)+c_1} \\ y(x)\to 1 \\ \end{align*}