64.5.35 problem 39

Internal problem ID [13348]
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
Date solved : Tuesday, January 28, 2025 at 05:31:22 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=\left (1-x \right ) y^{2}+\left (2 x -1\right ) y-x \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 31

dsolve(diff(y(x),x)=(1-x)*y(x)^2+(2*x-1)*y(x)-x,y(x), singsol=all)
 

\[ y = \frac {\left (2 x -2\right ) {\mathrm e}^{x}-c_{1}}{\left (2 x -4\right ) {\mathrm e}^{x}-c_{1}} \]

✓ Solution by Mathematica

Time used: 0.198 (sec). Leaf size: 28

DSolve[D[y[x],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*}