10.7.6 problem 6

Internal problem ID [1254]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant Coefficients, page 144
Problem number : 6
Date solved : Monday, January 27, 2025 at 04:47:58 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

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

\[ y = c_1 \,{\mathrm e}^{\frac {3 x}{2}}+c_2 \,{\mathrm e}^{-\frac {3 x}{2}} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 24

DSolve[4*D[y[x],{x,2}]-9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x/2} \left (c_1 e^{3 x}+c_2\right ) \]