82.54.4 problem Ex. 4

Internal problem ID [19020]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IX. Equations of the second order. problems at end of chapter at page 120
Problem number : Ex. 4
Date solved : Tuesday, January 28, 2025 at 12:45:55 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

dsolve((1+x^2)*diff(y(x),x$2)+3*x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 23

DSolve[(1+x^2)*D[y[x],{x,2}]+3*x*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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