Internal problem ID [11713]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+5 y^{\prime }+6 y={\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 5, y^{\prime }\left (0\right ) = 7] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = \frac {\left ({\mathrm e}^{4 x}+260 \,{\mathrm e}^{x}-201\right ) {\mathrm e}^{-3 x}}{12} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 26
DSolve[{y''[x]+5*y'[x]+6*y[x]==Exp[x],{y[0]==5,y'[0]==7}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{12} e^{-3 x} \left (260 e^x+e^{4 x}-201\right ) \]