35.5.12 problem 20

Internal problem ID [6146]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 5. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND ZERO RIGHT-HAND SIDE. page 414
Problem number : 20
Date solved : Monday, January 27, 2025 at 01:38:25 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)+(1+2*I)*diff(y(x),x)+(I-1)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}]+(1+2*I)*D[y[x],x]+(I-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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