13.8.5 problem 4

Internal problem ID [2380]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.2.1, Complex roots. Page 141
Problem number : 4
Date solved : Monday, January 27, 2025 at 05:50:52 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }-y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

dsolve(4*diff(y(t),t$2)-diff(y(t),t)+y(t)=0,y(t), singsol=all)
 

\[ y = {\mathrm e}^{\frac {t}{8}} \left (c_1 \sin \left (\frac {\sqrt {15}\, t}{8}\right )+c_2 \cos \left (\frac {\sqrt {15}\, t}{8}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 42

DSolve[4*D[y[t],{t,2}]-D[y[t],t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{t/8} \left (c_2 \cos \left (\frac {\sqrt {15} t}{8}\right )+c_1 \sin \left (\frac {\sqrt {15} t}{8}\right )\right ) \]