73.14.6 problem 21.8

Internal problem ID [15345]
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 : 21.8
Date solved : Monday, March 31, 2025 at 01:34:56 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-6 \,{\mathrm e}^{4 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=8 \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)-10*y(x) = -6*exp(4*x); 
ic:=y(0) = 6, D(y)(0) = 8; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 3 \,{\mathrm e}^{-2 x}+2 \,{\mathrm e}^{5 x}+{\mathrm e}^{4 x} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 25

ode=D[y[x],{x,2}]-3*D[y[x],x]-10*y[x]==-6*Exp[4*x]; 
ic={y[0]==6,Derivative[1][y][0] ==8}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-2 x} \left (e^{6 x}+2 e^{7 x}+3\right ) \]

✓ Sympy. Time used: 0.225 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-10*y(x) + 6*exp(4*x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 6, Subs(Derivative(y(x), x), x, 0): 8} 
dsolve(ode,func=y(x),ics=ics)
 

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