Internal problem ID [1721]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2, linear equations with constant coefficients. Page 138
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime }+y^{\prime }-10 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 5, y^{\prime }\relax (1) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 21
dsolve([2*diff(y(t),t$2)+diff(y(t),t)-10*y(t)=0,y(1) = 5, D(y)(1) = 2],y(t), singsol=all)
\[ y \relax (t ) = \frac {16 \,{\mathrm e}^{\frac {5}{2}-\frac {5 t}{2}}}{9}+\frac {29 \,{\mathrm e}^{2 t -2}}{9} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 30
DSolve[{2*y''[t]+y'[t]-10*y[t]==0,{y[1]==5,y'[1]==2}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {16}{9} e^{-\frac {5}{2} (t-1)}+\frac {29}{9} e^{2 t-2} \\ \end{align*}