Internal problem ID [1732]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.1, Complex roots. Page 141
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime }-y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(4*diff(y(t),t$2)-diff(y(t),t)+y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} {\mathrm e}^{\frac {t}{8}} \sin \left (\frac {\sqrt {15}\, t}{8}\right )+c_{2} {\mathrm e}^{\frac {t}{8}} \cos \left (\frac {\sqrt {15}\, t}{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 42
DSolve[4*y''[t]-y'[t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{t/8} \left (c_2 \cos \left (\frac {\sqrt {15} t}{8}\right )+c_1 \sin \left (\frac {\sqrt {15} t}{8}\right )\right ) \\ \end{align*}