67.8.35 problem 13.6 (a)

Internal problem ID [16530]
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 : 13.6 (a)
Date solved : Thursday, October 02, 2025 at 01:36:05 PM
CAS classification : [[_2nd_order, _missing_y]]

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

With initial conditions

\begin{align*} y \left (1\right )&=8 \\ y^{\prime }\left (1\right )&=-3 \\ \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 14

ode:=x*diff(diff(y(x),x),x)+4*diff(y(x),x) = 18*x^2; 
ic:=[y(1) = 8, D(y)(1) = -3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = x^{3}+\frac {2}{x^{3}}+5 \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 15

ode=x*D[y[x],{x,2}]+4*D[y[x],x]==18*x^2; 
ic={y[1]==8,Derivative[1][y][1]==-3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^3+\frac {2}{x^3}+5 \end{align*}

✓ Sympy. Time used: 0.129 (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 = {y(1): 8, Subs(Derivative(y(x), x), x, 1): -3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{3} + 5 + \frac {2}{x^{3}} \]