67.9.8 problem 14.1 (h)

Internal problem ID [16556]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 14. Higher order equations and the reduction of order method. Additional exercises page 277
Problem number : 14.1 (h)
Date solved : Thursday, October 02, 2025 at 01:36:27 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=2 y^{\prime }-5 y+30 \,{\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=diff(diff(y(x),x),x) = 2*diff(y(x),x)-5*y(x)+30*exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (\sin \left (2 x \right ) c_2 +\cos \left (2 x \right ) c_1 +\frac {15 \,{\mathrm e}^{2 x}}{4}\right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 35

ode=D[y[x],{x,2}]==2*D[y[x],x]-5*y[x]+30*Exp[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {15 e^{3 x}}{4}+c_2 e^x \cos (2 x)+c_1 e^x \sin (2 x) \end{align*}

✓ Sympy. Time used: 0.131 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) - 30*exp(3*x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} \sin {\left (2 x \right )} + C_{2} \cos {\left (2 x \right )} + \frac {15 e^{2 x}}{4}\right ) e^{x} \]