Internal problem ID [667]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page
172
Problem number: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime }+12 y^{\prime }+9 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = -4] \end {align*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 15
dsolve([4*diff(y(t),t$2)+12*diff(y(t),t)+9*y(t) = 0,y(0) = 1, D(y)(0) = -4],y(t), singsol=all)
\[ y \relax (t ) = -\frac {{\mathrm e}^{-\frac {3 t}{2}} \left (-2+5 t \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 21
DSolve[{4*y''[t]+12*y'[t]+9*y[t]==0,{y[0]==1,y'[0]==-4}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} e^{-3 t/2} (2-5 t) \\ \end{align*}