Internal problem ID [13856]
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 (h).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+5 y^{\prime }+6 y={\mathrm e}^{4 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 4.953 (sec). Leaf size: 23
dsolve([diff(y(t),t$2)+5*diff(y(t),t)+6*y(t)=exp(4*t),y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left ({\mathrm e}^{7 t}+119 \,{\mathrm e}^{t}-78\right ) {\mathrm e}^{-3 t}}{42} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 26
DSolve[{y''[t]+5*y'[t]+6*y[t]==Exp[4*t],{y[0]==1,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{42} e^{-3 t} \left (119 e^t+e^{7 t}-78\right ) \]