64.1.4 problem 1(d)

Internal problem ID [13249]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number : 1(d)
Date solved : Tuesday, January 28, 2025 at 05:13:03 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

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

\[ y = \frac {c_{1} x +c_{2}}{x^{2}+1} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 20

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

\[ y(x)\to \frac {c_2 x+c_1}{x^2+1} \]