Internal problem ID [2852]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for
10.4. page 689
Problem number: Problem 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }=30 \,{\mathrm e}^{-3 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 2.781 (sec). Leaf size: 18
dsolve([diff(y(t),t$2)-2*diff(y(t),t)=30*exp(-3*t),y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \left (3 \,{\mathrm e}^{5 t}-4 \,{\mathrm e}^{3 t}+2\right ) {\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 21
DSolve[{y''[t]-2*y'[t]==30*Exp[-3*t],{y[0]==1,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 2 e^{-3 t}+3 e^{2 t}-4 \]