64.13.28 problem 28

Internal problem ID [13487]
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 : Monday, March 31, 2025 at 07:59:26 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*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

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

\[ y = \frac {c_1 +c_2 \left (x +2\right )^{4}}{x +2} \]

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

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

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

✓ Sympy. Time used: 0.226 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 2)**2*Derivative(y(x), (x, 2)) - (x + 2)*Derivative(y(x), x) - 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \left (x + 2\right ) \]