73.16.16 problem 24.2 (b)

Internal problem ID [15457]
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 (b)
Date solved : Monday, March 31, 2025 at 01:38:27 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=12 \,{\mathrm e}^{2 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=8 \end{align*}

✓ Maple. Time used: 0.026 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)-diff(y(x),x)-6*y(x) = 12*exp(2*x); 
ic:=y(0) = 0, D(y)(0) = 8; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 4 \,{\mathrm e}^{3 x}-{\mathrm e}^{-2 x}-3 \,{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 27

ode=D[y[x],{x,2}]-D[y[x],x]-6*y[x]==12*Exp[2*x]; 
ic={y[0]==0,Derivative[1][y][0] ==8}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-2 x} \left (-3 e^{4 x}+4 e^{5 x}-1\right ) \]

✓ Sympy. Time used: 0.216 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = 4 e^{3 x} - 3 e^{2 x} - e^{- 2 x} \]