64.8.2 problem 1 (b)

Internal problem ID [13390]
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 : Tuesday, January 28, 2025 at 05:36:53 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*}

✓ Solution by Maple

Time used: 0.179 (sec). Leaf size: 63

dsolve([diff(y(x),x$2)+5*diff(y(x),x)+6*y(x)=exp(x),y(0) = 5, D(y)(1) = 7],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 68

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

\[ y(x)\to \frac {e^{-3 x} \left (-177 e^x-3 e^{4 x}-84 e^{x+3}+e^{x+4}+2 e^{4 x+1}+118 e+84 e^3-e^4\right )}{12 (2 e-3)} \]