73.15.79 problem 22.15 (f)

Internal problem ID [15439]
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 (f)
Date solved : Monday, March 31, 2025 at 01:37:46 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=\frac {10}{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=2*x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)+y(x) = 10/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-10 \sqrt {x}\, \ln \left (x \right )+c_2 x +\left (c_1 -20\right ) \sqrt {x}}{x^{{3}/{2}}} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 25

ode=2*x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+y[x]==10/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {-10 \log (x)+c_2 \sqrt {x}-20+c_1}{x} \]

✓ Sympy. Time used: 0.268 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) + 5*x*Derivative(y(x), x) + y(x) - 10/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x} + \frac {C_{2}}{\sqrt {x}} - \frac {10 \log {\left (x \right )}}{x} \]