67.16.17 problem 24.3 (a)

Internal problem ID [16816]
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 : 24.3 (a)
Date solved : Thursday, October 02, 2025 at 01:39:22 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=30 \,{\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

ode:=diff(diff(diff(y(x),x),x),x)-4*diff(y(x),x) = 30*exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{-2 x} c_2}{2}+\frac {{\mathrm e}^{2 x} c_1}{2}+2 \,{\mathrm e}^{3 x}+c_3 \]

✓ Mathematica. Time used: 0.048 (sec). Leaf size: 37

ode=D[y[x],{x,3}]-4*D[y[x],x]==30*Exp[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 e^{3 x}+\frac {1}{2} c_1 e^{2 x}-\frac {1}{2} c_2 e^{-2 x}+c_3 \end{align*}

✓ Sympy. Time used: 0.123 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-30*exp(3*x) - 4*Derivative(y(x), x) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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