7.10.39 problem 45

Internal problem ID [309]
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 : 45
Date solved : Wednesday, February 05, 2025 at 03:18:20 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 i y^{\prime }+3 y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)+2*I*diff(y(x),x)+3*y(x)=0,y(x), singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{i x}+c_2 \,{\mathrm e}^{-3 i x} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 26

DSolve[D[y[x],{x,2}]+2*I*D[y[x],x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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