Internal problem ID [13853]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 27. Differentiation and the Laplace transform. Additional Exercises. page
496
Problem number: 27.1 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+4 y=20 \,{\mathrm e}^{4 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 12] \end {align*}
✓ Solution by Maple
Time used: 4.954 (sec). Leaf size: 21
dsolve([diff(y(t),t$2)+4*y(t)=20*exp(4*t),y(0) = 3, D(y)(0) = 12],y(t), singsol=all)
\[ y \left (t \right ) = 2 \cos \left (2 t \right )+4 \sin \left (2 t \right )+{\mathrm e}^{4 t} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 23
DSolve[{y''[t]+4*y[t]==20*Exp[4*t],{y[0]==3,y'[0]==12}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{4 t}+4 \sin (2 t)+2 \cos (2 t) \]