64.8.1 problem 1 (a)

Internal problem ID [13310]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page 113
Problem number : 1 (a)
Date solved : Wednesday, March 05, 2025 at 09:43:02 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=7 \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 20

ode:=diff(diff(y(x),x),x)+5*diff(y(x),x)+6*y(x) = exp(x); 
ic:=y(0) = 5, D(y)(0) = 7; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {\left ({\mathrm e}^{4 x}+260 \,{\mathrm e}^{x}-201\right ) {\mathrm e}^{-3 x}}{12} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 26

ode=D[y[x],{x,2}]+5*D[y[x],x]+6*y[x]==Exp[x]; 
ic={y[0]==5,Derivative[1][y][0] ==7}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{12} e^{-3 x} \left (260 e^x+e^{4 x}-201\right ) \]

✓ Sympy. Time used: 0.208 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) - exp(x) + 5*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 5, Subs(Derivative(y(x), x), x, 0): 7} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {e^{x}}{12} + \frac {65 e^{- 2 x}}{3} - \frac {67 e^{- 3 x}}{4} \]