Internal problem ID [13556]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 29. Convolution. Additional Exercises. page 523
Problem number: 29.6 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+4 y={\mathrm e}^{3 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 24
dsolve([diff(y(t),t$2)+4*y(t)=exp(3*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {2 \cos \left (t \right )^{2}}{13}-\frac {3 \sin \left (t \right ) \cos \left (t \right )}{13}+\frac {{\mathrm e}^{3 t}}{13}+\frac {1}{13} \]
✓ Solution by Mathematica
Time used: 0.1 (sec). Leaf size: 29
DSolve[{y''[t]+4*y[t]==Exp[3*t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{26} \left (2 e^{3 t}-3 \sin (2 t)-2 \cos (2 t)\right ) \]