58.8.2 problem 1 (b)

Internal problem ID [14671]
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 (b)
Date solved : Thursday, October 02, 2025 at 09:50:03 AM
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 (1\right )&=7 \\ \end{align*}

✓ Maple. Time used: 0.071 (sec). Leaf size: 58

ode:=diff(diff(y(x),x),x)+5*diff(y(x),x)+6*y(x) = exp(x); 
ic:=[y(0) = 5, D(y)(1) = 7]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\left (2 \,{\mathrm e}^{1+4 x}+{\mathrm e}^{4+x}-3 \,{\mathrm e}^{4 x}-84 \,{\mathrm e}^{3+x}-{\mathrm e}^{4}+84 \,{\mathrm e}^{3}-177 \,{\mathrm e}^{x}+118 \,{\mathrm e}\right ) {\mathrm e}^{-3 x}}{-36+24 \,{\mathrm e}} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 68

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

\begin{align*} y(x)&\to \frac {e^{-3 x} \left (-177 e^x-3 e^{4 x}-84 e^{x+3}+e^{x+4}+2 e^{4 x+1}+118 e+84 e^3-e^4\right )}{12 (2 e-3)} \end{align*}

✓ Sympy. Time used: 0.137 (sec). Leaf size: 54

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, 1): 7} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {e^{x}}{12} + \frac {\left (- 84 e^{3} - 177 + e^{4}\right ) e^{- 2 x}}{-36 + 24 e} + \frac {\left (- e^{4} + 118 e + 84 e^{3}\right ) e^{- 3 x}}{-36 + 24 e} \]