73.14.7 problem 21.9

Internal problem ID [15346]
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 : 21.9
Date solved : Monday, March 31, 2025 at 01:34:58 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=7 \,{\mathrm e}^{5 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=12\\ y^{\prime }\left (0\right )&=-2 \end{align*}

✓ Maple. Time used: 0.035 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)-10*y(x) = 7*exp(5*x); 
ic:=y(0) = 12, D(y)(0) = -2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = {\mathrm e}^{5 x} \left (x +3\right )+9 \,{\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 22

ode=D[y[x],{x,2}]-3*D[y[x],x]-10*y[x]==7*Exp[5*x]; 
ic={y[0]==12,Derivative[1][y][0] ==-2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-2 x} \left (e^{7 x} (x+3)+9\right ) \]

✓ Sympy. Time used: 0.255 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-10*y(x) - 7*exp(5*x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 12, Subs(Derivative(y(x), x), x, 0): -2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (x + 3\right ) e^{5 x} + 9 e^{- 2 x} \]