67.15.75 problem 22.15 (b)

Internal problem ID [16793]
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 (b)
Date solved : Thursday, October 02, 2025 at 01:38:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=\frac {50}{x^{3}} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 23

ode:=2*x^2*diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x) = 50/x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {14 x^{{7}/{2}} c_1 +14 c_2 \,x^{4}+25}{14 x^{3}} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 25

ode=2*x^2*D[y[x],{x,2}]-x*D[y[x],x]+y[x]==50/x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {25}{14 x^3}+c_1 \sqrt {x}+c_2 x \end{align*}

✓ Sympy. Time used: 0.238 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) - x*Derivative(y(x), x) + y(x) - 50/x**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sqrt {x} + C_{2} x + \frac {25}{14 x^{3}} \]