76.13.16 problem 16

Internal problem ID [17598]
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 : 16
Date solved : Tuesday, January 28, 2025 at 10:44:56 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+16*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x} \left (c_{1} \sin \left (2 \sqrt {3}\, x \right )+c_{2} \cos \left (2 \sqrt {3}\, x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 36

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (c_2 \cos \left (2 \sqrt {3} x\right )+c_1 \sin \left (2 \sqrt {3} x\right )\right ) \]