8.9.13 problem 45

Internal problem ID [857]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.3, second order linear equations. Page 323
Problem number : 45
Date solved : Wednesday, February 05, 2025 at 04:34:29 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: 0.002 (sec). Leaf size: 17

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

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

✓ 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]
 

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