7.10.41 problem 47

Internal problem ID [311]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 47
Date solved : Wednesday, February 05, 2025 at 03:18:22 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }&=\left (-2+2 i \sqrt {3}\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 30

dsolve(diff(y(x),x$2)=(-2+2*I*sqrt(3))*y(x),y(x), singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{\left (1+i \sqrt {3}\right ) x}+c_2 \,{\mathrm e}^{-\left (1+i \sqrt {3}\right ) x} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 41

DSolve[D[y[x],{x,2}]==(-2+2*I*Sqrt[3])*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{x+i \sqrt {3} x}+c_2 e^{\left (-1-i \sqrt {3}\right ) x} \]