64.5.8 problem 8

Internal problem ID [13321]
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 : 8
Date solved : Tuesday, January 28, 2025 at 05:22:07 AM
CAS classification : [_linear]

\begin{align*} \left (x^{2}+x -2\right ) y^{\prime }+3 \left (1+x \right ) y&=x -1 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 24

dsolve((x^2+x-2)*diff(y(x),x)+3*(x+1)*y(x)=x-1,y(x), singsol=all)
 

\[ y = \frac {\frac {\left (x -1\right )^{3}}{3}+c_{1}}{\left (x +2\right ) \left (x -1\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.087 (sec). Leaf size: 76

DSolve[(x^2+x-2)*D[y[x],x]+3*(x+1)*y[x]==x-1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x-\frac {3 (K[1]+1)}{K[1]^2+K[1]-2}dK[1]\right ) \left (\int _1^x\frac {\exp \left (-\int _1^{K[2]}-\frac {3 (K[1]+1)}{K[1]^2+K[1]-2}dK[1]\right )}{K[2]+2}dK[2]+c_1\right ) \]