Internal problem ID [1722]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2, linear equations with constant coefficients. Page 138
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {5 y^{\prime \prime }+5 y^{\prime }-y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 34
dsolve([5*diff(y(t),t$2)+5*diff(y(t),t)-y(t)=0,y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left ({\mathrm e}^{\frac {3 t \sqrt {5}}{10}-\frac {t}{2}}-{\mathrm e}^{-\frac {t}{2}-\frac {3 t \sqrt {5}}{10}}\right ) \sqrt {5}}{3} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 32
DSolve[{5*y''[t]+5*y'[t]-y[t]==0,{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {2}{3} \sqrt {5} e^{-t/2} \sinh \left (\frac {3 t}{2 \sqrt {5}}\right ) \\ \end{align*}