87.13.11 problem 11

Internal problem ID [23494]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 100
Problem number : 11
Date solved : Thursday, October 02, 2025 at 09:42:25 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 29

ode:=(x+3)^2*diff(diff(y(x),x),x)+3*(x+3)*diff(y(x),x)+5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \sin \left (2 \ln \left (x +3\right )\right )+c_2 \cos \left (2 \ln \left (x +3\right )\right )}{x +3} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 32

ode=(x+3)^2*D[y[x],{x,2}]+3*(x+3)*D[y[x],x]+5*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_2 \cos (2 \log (x+3))+c_1 \sin (2 \log (x+3))}{x+3} \end{align*}

✓ Sympy. Time used: 0.161 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 3)**2*Derivative(y(x), (x, 2)) + (3*x + 9)*Derivative(y(x), x) + 5*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x + 3} \]