Internal problem ID [13553]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 28. The inverse Laplace transform. Additional Exercises. page 509
Problem number: 28.9 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+13 y={\mathrm e}^{2 t} \sin \left (3 t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 4, y^{\prime }\left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 26
dsolve([diff(y(t),t$2)-4*diff(y(t),t)+13*y(t)=exp(2*t)*sin(3*t),y(0) = 4, D(y)(0) = 3],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {{\mathrm e}^{2 t} \left (-24+t \right ) \cos \left (3 t \right )}{6}-\frac {29 \,{\mathrm e}^{2 t} \sin \left (3 t \right )}{18} \]
✓ Solution by Mathematica
Time used: 0.13 (sec). Leaf size: 30
DSolve[{y''[t]-4*y'[t]+13*y[t]==Exp[2*t]*Sin[3*t],{y[0]==4,y'[0]==3}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {1}{18} e^{2 t} (29 \sin (3 t)+3 (t-24) \cos (3 t)) \]