67.16.4 problem 24.1 (d)

Internal problem ID [16803]
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 : 24.1 (d)
Date solved : Thursday, October 02, 2025 at 01:39:08 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=6 \,{\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)-7*diff(y(x),x)+10*y(x) = 6*exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 27

ode=D[y[x],{x,2}]-7*D[y[x],x]+10*y[x]==6*Exp[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.120 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(10*y(x) - 6*exp(3*x) - 7*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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