Internal problem ID [1740]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.2, Equal roots, reduction of order. Page 147
Problem number: 2.
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*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 18
dsolve(4*diff(y(t),t$2)-12*diff(y(t),t)+9*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} {\mathrm e}^{\frac {3 t}{2}}+c_{2} {\mathrm e}^{\frac {3 t}{2}} t \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 20
DSolve[4*y''[t]-12*y'[t]+9*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{3 t/2} (c_2 t+c_1) \\ \end{align*}