76.13.14 problem 14

Internal problem ID [17596]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 10:44:52 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (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: 0.012 (sec). Leaf size: 24

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

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