Internal problem ID [11714]
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).
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 (1\right ) = 7] \end {align*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 55
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)
\[ y \left (x \right ) = \frac {\left (-{\mathrm e}^{4-x}+84 \,{\mathrm e}^{3-x}+{\mathrm e}^{4}+2 \,{\mathrm e}^{3 x +1}-84 \,{\mathrm e}^{3}+118 \,{\mathrm e}^{1-x}-3 \,{\mathrm e}^{3 x}-177\right ) {\mathrm e}^{-2 x}}{24 \,{\mathrm e}-36} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 68
DSolve[{y''[x]+5*y'[x]+6*y[x]==Exp[x],{y[0]==5,y'[1]==7}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-3 x} \left (-177 e^x-3 e^{4 x}-84 e^{x+3}+e^{x+4}+2 e^{4 x+1}+118 e+84 e^3-e^4\right )}{12 (2 e-3)} \]