67.14.1 problem 21.5 (i)

Internal problem ID [16698]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 21. Nonhomogeneous equations in general. Additional exercises page 391
Problem number : 21.5 (i)
Date solved : Thursday, October 02, 2025 at 01:37:50 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

With initial conditions

\begin{align*} y \left (0\right )&=6 \\ y^{\prime }\left (0\right )&=6 \\ \end{align*}

✓ Maple. Time used: 0.031 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+4*y(x) = 24*exp(2*x); 
ic:=[y(0) = 6, D(y)(0) = 6]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 3 \cos \left (2 x \right )+3 \,{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 17

ode=D[y[x],{x,2}]+4*y[x]==24*Exp[2*x]; 
ic={y[0]==6,Derivative[1][y][0] ==6}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3 \left (e^{2 x}+\cos (2 x)\right ) \end{align*}

✓ Sympy. Time used: 0.048 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) - 24*exp(2*x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 6, Subs(Derivative(y(x), x), x, 0): 6} 
dsolve(ode,func=y(x),ics=ics)
 

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