76.13.11 problem 11

Internal problem ID [17593]
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 : 11
Date solved : Tuesday, January 28, 2025 at 10:44:46 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)+2*diff(y(x),x)-8*y(x)=0,y(x), singsol=all)
 

\[ y = \left ({\mathrm e}^{6 x} c_{1} +c_{2} \right ) {\mathrm e}^{-4 x} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}]+2*D[y[x],x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-4 x} \left (c_2 e^{6 x}+c_1\right ) \]