64.13.22 problem 22

Internal problem ID [13552]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number : 22
Date solved : Tuesday, January 28, 2025 at 05:52:43 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 15

dsolve([x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+3*y(x)=0,y(1) = 1, D(y)(1) = -5],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 16

DSolve[{x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+3*y[x]==0,{y[1]==1,Derivative[1][y][1]==-5}},y[x],x,IncludeSingularSolutions -> True]
 

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