64.5.7 problem 7

Internal problem ID [13320]
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 : 7
Date solved : Tuesday, January 28, 2025 at 05:22:06 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.142 (sec). Leaf size: 80

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

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