64.4.1 problem 1

Internal problem ID [13290]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 05:16:06 AM
CAS classification : [_separable]

\begin{align*} 4 y x +\left (x^{2}+1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

dsolve((4*x*y(x))+(x^2+1)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 20

DSolve[(4*x*y[x])+(x^2+1)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {c_1}{\left (x^2+1\right )^2} \\ y(x)\to 0 \\ \end{align*}