67.8.1 problem 13.1 (a)

Internal problem ID [16496]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.1 (a)
Date solved : Thursday, October 02, 2025 at 01:35:34 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }+4 y^{\prime }&=18 x^{2} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=x*diff(diff(y(x),x),x)+4*diff(y(x),x) = 18*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{3}-\frac {c_1}{3 x^{3}}+c_2 \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 20

ode=x*D[y[x],{x,2}]+4*D[y[x],x]==18*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^3-\frac {c_1}{3 x^3}+c_2 \end{align*}

✓ Sympy. Time used: 0.120 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-18*x**2 + x*Derivative(y(x), (x, 2)) + 4*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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