7.10.40 problem 46

Internal problem ID [310]
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 : 46
Date solved : Wednesday, February 05, 2025 at 03:18:21 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-i y^{\prime }+6 y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)-I*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{-2 i x}+c_2 \,{\mathrm e}^{3 i x} \]

✓ Solution by Mathematica

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

DSolve[D[y[x],{x,2}]-I*D[y[x],x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 i x} \left (c_1 e^{5 i x}+c_2\right ) \]