64.5.22 problem 22

Internal problem ID [13335]
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 : 22
Date solved : Tuesday, January 28, 2025 at 05:22:44 AM
CAS classification : [_separable]

\begin{align*} 2 x \left (y+1\right )-\left (x^{2}+1\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=-5 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 11

dsolve([2*x*(y(x)+1)-(x^2+1)*diff(y(x),x)=0,y(1) = -5],y(x), singsol=all)
 

\[ y = -2 x^{2}-3 \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 12

DSolve[{2*x*(y[x]+1)-(x^2+1)*D[y[x],x]==0,{y[1]==-5}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -2 x^2-3 \]