64.13.28 problem 28

Internal problem ID [13558]
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 : 28
Date solved : Tuesday, January 28, 2025 at 05:52:56 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

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

\[ y = \frac {c_{1} +\left (x +2\right )^{4} c_{2}}{x +2} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 22

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

\[ y(x)\to c_1 (x+2)^3+\frac {c_2}{x+2} \]