Internal problem ID [2339]
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 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-3 y^{\prime }+2 y-4=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 16
dsolve([diff(y(t),t$2)-3*diff(y(t),t)+2*y(t)=4,y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = 3 \,{\mathrm e}^{2 t}-5 \,{\mathrm e}^{t}+2 \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[{y''[t]-3*y'[t]+2*y[t]==4,{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \left (e^t-1\right ) \left (3 e^t-2\right ) \\ \end{align*}