Internal problem ID [12771]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+\left (-3-4 i\right ) y^{\prime \prime }+\left (-4+12 i\right ) y^{\prime }+12 y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
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)
\[ y \left (x \right ) = \left (c_{3} x +c_{2} \right ) {\mathrm e}^{2 i x}+c_{1} {\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 29
DSolve[y'''[x]-(3+4*I)*y''[x]-(4-12*I)*y'[x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 i x} (c_2 x+c_1)+c_3 e^{3 x} \]