Internal problem ID [11805]
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: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+13 y=18 \,{\mathrm e}^{-2 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve([diff(y(x),x$2)+4*diff(y(x),x)+13*y(x)=18*exp(-2*x),y(0) = 0, D(y)(0) = 4],y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 \,{\mathrm e}^{-2 x} \left (2 \sin \left (3 x \right )-3 \cos \left (3 x \right )+3\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 28
DSolve[{y''[x]+4*y'[x]+13*y[x]==18*Exp[-2*x],{y[0]==0,y'[0]==4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} e^{-2 x} (4 \sin (3 x)-6 \cos (3 x)+6) \]