Internal problem ID [1720]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2, linear equations with constant coefficients. Page 138
Problem number: 5.
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 }-4 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve([diff(y(t),t$2)-3*diff(y(t),t)-4*y(t)=0,y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \frac {{\mathrm e}^{4 t}}{5}+\frac {4 \,{\mathrm e}^{-t}}{5} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 21
DSolve[{y''[t]-3*y'[t]-4*y[t]==0,{y[0]==1,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{5} e^{-t} \left (e^{5 t}+4\right ) \\ \end{align*}