Internal problem ID [11804]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page
151
Problem number: 30.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+9 y=27 \,{\mathrm e}^{-6 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = -2, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve([diff(y(x),x$2)+6*diff(y(x),x)+9*y(x)=27*exp(-6*x),y(0) = -2, D(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \left (3 x -5\right ) {\mathrm e}^{-3 x}+3 \,{\mathrm e}^{-6 x} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 24
DSolve[{y''[x]+6*y'[x]+9*y[x]==27*Exp[-6*x],{y[0]==-2,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-6 x} \left (e^{3 x} (3 x-5)+3\right ) \]