67.16.15 problem 24.2 (a)

Internal problem ID [16814]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 24. Variation of parameters. Additional exercises page 444
Problem number : 24.2 (a)
Date solved : Thursday, October 02, 2025 at 01:39:20 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y&=\frac {10}{x} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=3 \\ y^{\prime }\left (1\right )&=-15 \\ \end{align*}

✓ Maple. Time used: 0.033 (sec). Leaf size: 19

ode:=x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)-4*y(x) = 10/x; 
ic:=[y(1) = 3, D(y)(1) = -15]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 20

ode=x^2*D[y[x],{x,2}]-2*x*D[y[x],x]-4*y[x]==10/x; 
ic={y[1]==3,Derivative[1][y][1]==-15}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.301 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 2*x*Derivative(y(x), x) - 4*y(x) - 10/x,0) 
ics = {y(1): 3, Subs(Derivative(y(x), x), x, 1): -15} 
dsolve(ode,func=y(x),ics=ics)
 

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