23.2.9 problem 4(i)

Internal problem ID [4126]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 3. Linear differential equations of second order. Exercises at page 31
Problem number : 4(i)
Date solved : Monday, January 27, 2025 at 08:36:56 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(x),x$2)+diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{-\frac {x}{8}} \left (c_{1} \sin \left (\frac {\sqrt {15}\, x}{8}\right )+c_{2} \cos \left (\frac {\sqrt {15}\, x}{8}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 42

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

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