64.6.3 problem 3

Internal problem ID [13353]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 05:31:34 AM
CAS classification : [_separable]

\begin{align*} y-1+x \left (1+x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

dsolve((y(x)-1)+(x*(x+1))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} x +c_{1} -1}{x} \]

✓ Solution by Mathematica

Time used: 0.189 (sec). Leaf size: 74

DSolve[(y[x]-1)+(x*(x+1))*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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