20.10.6 problem Problem 19

Internal problem ID [3778]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.8, A Differential Equation with Nonconstant Coefficients. page 567
Problem number : Problem 19
Date solved : Sunday, March 30, 2025 at 02:08:16 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+6 x y^{\prime }+6 y&=4 \,{\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=x^2*diff(diff(y(x),x),x)+6*x*diff(y(x),x)+6*y(x) = 4*exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (x -1\right ) {\mathrm e}^{2 x}+c_2 x -c_1}{x^{3}} \]

✓ Mathematica. Time used: 0.052 (sec). Leaf size: 25

ode=x^2*D[y[x],{x,2}]+6*x*D[y[x],x]+6*y[x]==4*Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {e^{2 x} (x-1)+c_2 x+c_1}{x^3} \]

✓ Sympy. Time used: 0.561 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 6*x*Derivative(y(x), x) + 6*y(x) - 4*exp(2*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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