10.8.6 problem 12

Internal problem ID [1278]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.3 Complex Roots of the Characteristic Equation , page 164
Problem number : 12
Date solved : Monday, January 27, 2025 at 04:49:29 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }+9 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 17

dsolve(4*diff(y(x),x$2) +9*y(x) = 0,y(x), singsol=all)
 

\[ y = c_1 \sin \left (\frac {3 x}{2}\right )+c_2 \cos \left (\frac {3 x}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 20

DSolve[D[y[x],{x,2}]+9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cos (3 x)+c_2 \sin (3 x) \]