85.67.15 problem 15

Internal problem ID [22906]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 216
Problem number : 15
Date solved : Thursday, October 02, 2025 at 09:16:28 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y&=24+24 x \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 22

ode:=x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+4*y(x) = 24+24*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \,x^{4}+c_1 x -\frac {8 x}{3}+6-8 \ln \left (x \right ) x \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 26

ode=x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+4*y[x]==24*(x+1); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 x^4-8 x \log (x)+\left (-\frac {8}{3}+c_1\right ) x+6 \end{align*}

✓ Sympy. Time used: 0.162 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 4*x*Derivative(y(x), x) - 24*x + 4*y(x) - 24,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x + C_{2} x^{4} - 8 x \log {\left (x \right )} + 6 \]