Internal problem ID [1736]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.1, Complex roots. Page 141
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {3 y^{\prime \prime }-2 y^{\prime }+4 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (2) = 1, y^{\prime }\relax (2) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 70
dsolve([3*diff(y(t),t$2)-2*diff(y(t),t)+4*y(t)=0,y(2) = 1, D(y)(2) = -1],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (\left (\cos \left (\frac {2 \sqrt {11}}{3}\right ) \sqrt {11}+4 \sin \left (\frac {2 \sqrt {11}}{3}\right )\right ) \cos \left (\frac {\sqrt {11}\, t}{3}\right )+\sin \left (\frac {\sqrt {11}\, t}{3}\right ) \left (\sin \left (\frac {2 \sqrt {11}}{3}\right ) \sqrt {11}-4 \cos \left (\frac {2 \sqrt {11}}{3}\right )\right )\right ) {\mathrm e}^{\frac {t}{3}-\frac {2}{3}} \sqrt {11}}{11} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 54
DSolve[{3*y''[t]-2*y'[t]+4*y[t]==0,{y[2]==1,y'[2]==-1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{11} e^{\frac {t-2}{3}} \left (11 \cos \left (\frac {1}{3} \sqrt {11} (t-2)\right )-4 \sqrt {11} \sin \left (\frac {1}{3} \sqrt {11} (t-2)\right )\right ) \\ \end{align*}