67.15.74 problem 22.15 (a)

Internal problem ID [16792]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.15 (a)
Date solved : Thursday, October 02, 2025 at 01:38:54 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y&=\frac {5}{x^{3}} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 20

ode:=x^2*diff(diff(y(x),x),x)-5*x*diff(y(x),x)+8*y(x) = 5/x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \,x^{2}+c_1 \,x^{4}+\frac {1}{7 x^{3}} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 25

ode=x^2*D[y[x],{x,2}]-5*x*D[y[x],x]+8*y[x]==5/x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 x^4+\frac {1}{7 x^3}+c_1 x^2 \end{align*}

✓ Sympy. Time used: 0.239 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 5*x*Derivative(y(x), x) + 8*y(x) - 5/x**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x^{2} + C_{2} x^{4} + \frac {1}{7 x^{3}} \]