67.14.13 problem 21.13 (c)

Internal problem ID [16710]
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 : 21.13 (c)
Date solved : Thursday, October 02, 2025 at 01:38:00 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-18 \,{\mathrm e}^{4 x}+14 \,{\mathrm e}^{5 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 31

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)-10*y(x) = -18*exp(4*x)+14*exp(5*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (14 x +7 c_2 -2\right ) {\mathrm e}^{5 x}}{7}+{\mathrm e}^{-2 x} c_1 +3 \,{\mathrm e}^{4 x} \]

✓ Mathematica. Time used: 0.054 (sec). Leaf size: 36

ode=D[y[x],{x,2}]-3*D[y[x],x]-10*y[x]==-18*Exp[4*x]+14*Exp[5*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3 e^{4 x}+c_1 e^{-2 x}+e^{5 x} \left (2 x-\frac {2}{7}+c_2\right ) \end{align*}

✓ Sympy. Time used: 0.157 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-10*y(x) - 14*exp(5*x) + 18*exp(4*x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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