76.13.24 problem 24

Internal problem ID [17606]
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 : 24
Date solved : Tuesday, January 28, 2025 at 10:45:12 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

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

\[ y = \left (c_{2} {\mathrm e}^{\frac {15 x}{4}}+c_{1} \right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

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

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

\[ y(x)\to c_1 e^{3 x/4}+c_2 e^{-3 x} \]