64.8.1 problem 1 (a)

Internal problem ID [13389]
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 : Tuesday, January 28, 2025 at 05:36:51 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 (0\right )&=7 \end{align*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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