71.10.12 problem 17

Internal problem ID [14507]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number : 17
Date solved : Tuesday, January 28, 2025 at 06:42:47 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+\left (-3-4 i\right ) y^{\prime \prime }+\left (-4+12 i\right ) y^{\prime }+12 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(x),x$3)-(3+4*I)*diff(y(x),x$2)-(4-12*I)*diff(y(x),x)+12*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_{3} x +c_{2} \right ) {\mathrm e}^{2 i x}+{\mathrm e}^{3 x} c_{1} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 29

DSolve[D[y[x],{x,3}]-(3+4*I)*D[y[x],{x,2}]-(4-12*I)*D[y[x],x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 i x} (c_2 x+c_1)+c_3 e^{3 x} \]