20.9.20 problem Problem 20

Internal problem ID [3764]
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 8.7, The Variation of Parameters Method. page 556
Problem number : Problem 20
Date solved : Sunday, March 30, 2025 at 02:07:42 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=36 \,{\mathrm e}^{2 x} \ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 31

ode:=diff(diff(diff(y(x),x),x),x)-6*diff(diff(y(x),x),x)+12*diff(y(x),x)-8*y(x) = 36*exp(2*x)*ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} \left (6 x^{3} \ln \left (x \right )+c_3 \,x^{2}-11 x^{3}+c_2 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 36

ode=D[y[x],{x,3}]-6*D[y[x],{x,2}]+12*D[y[x],x]-8*y[x]==36*Exp[2*x]*Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{2 x} \left (-11 x^3+6 x^3 \log (x)+c_3 x^2+c_2 x+c_1\right ) \]

✓ Sympy. Time used: 0.359 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*y(x) - 36*exp(2*x)*log(x) + 12*Derivative(y(x), x) - 6*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + x \left (C_{2} + x \left (C_{3} + 6 x \log {\left (x \right )} - 11 x\right )\right )\right ) e^{2 x} \]