Internal problem ID [1735]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.1, Complex roots. Page 141
Problem number: 8.
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 }+3 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1, y^{\prime }\relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.115 (sec). Leaf size: 70
dsolve([2*diff(y(t),t$2)-diff(y(t),t)+3*y(t)=0,y(1) = 1, D(y)(1) = 1],y(t), singsol=all)
\[ y \relax (t ) = \frac {{\mathrm e}^{\frac {t}{4}-\frac {1}{4}} \sqrt {23}\, \left (\left (\cos \left (\frac {\sqrt {23}}{4}\right ) \sqrt {23}-3 \sin \left (\frac {\sqrt {23}}{4}\right )\right ) \cos \left (\frac {\sqrt {23}\, t}{4}\right )+\sin \left (\frac {\sqrt {23}\, t}{4}\right ) \left (\sin \left (\frac {\sqrt {23}}{4}\right ) \sqrt {23}+3 \cos \left (\frac {\sqrt {23}}{4}\right )\right )\right )}{23} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 54
DSolve[{2*y''[t]-y'[t]+3*y[t]==0,{y[1]==1,y'[1]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{23} e^{\frac {t-1}{4}} \left (3 \sqrt {23} \sin \left (\frac {1}{4} \sqrt {23} (t-1)\right )+23 \cos \left (\frac {1}{4} \sqrt {23} (t-1)\right )\right ) \\ \end{align*}