73.14.11 problem 21.13 (a)

Internal problem ID [15350]
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 (a)
Date solved : Monday, March 31, 2025 at 01:35:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&={\mathrm e}^{4 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

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

\[ y = \frac {\left (6 \,{\mathrm e}^{7 x} c_2 -{\mathrm e}^{6 x}+6 c_1 \right ) {\mathrm e}^{-2 x}}{6} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 31

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

\[ y(x)\to -\frac {e^{4 x}}{6}+c_1 e^{-2 x}+c_2 e^{5 x} \]

✓ Sympy. Time used: 0.209 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + C_{2} e^{5 x} - \frac {e^{4 x}}{6} \]