73.16.8 problem 24.1 (h)

Internal problem ID [15449]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 24. Variation of parameters. Additional exercises page 444
Problem number : 24.1 (h)
Date solved : Monday, March 31, 2025 at 01:38:08 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=12 x^{3} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 29

ode:=x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-9*y(x) = 12*x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {6 x^{6} \ln \left (x \right )+\left (3 c_1 -1\right ) x^{6}+3 c_2}{3 x^{3}} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 29

ode=x^2*D[y[x],{x,2}]+x*D[y[x],x]-9*y[x]==12*x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 2 x^3 \log (x)+\left (-\frac {1}{3}+c_2\right ) x^3+\frac {c_1}{x^3} \]

✓ Sympy. Time used: 0.271 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-12*x**3 + x**2*Derivative(y(x), (x, 2)) + x*Derivative(y(x), x) - 9*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + x^{6} \left (C_{2} + 2 \log {\left (x \right )}\right )}{x^{3}} \]