Internal problem ID [12452]
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: 18.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+\left (-3-i\right ) y^{\prime \prime \prime }+\left (4+3 i\right ) y^{\prime \prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$4)-(3+I)*diff(y(x),x$3)+(4+3*I)*diff(y(x),x$2)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{\left (2-i\right ) x}+c_{2} {\mathrm e}^{\left (1+2 i\right ) x}+c_{3} +c_{4} x \]
✓ Solution by Mathematica
Time used: 0.156 (sec). Leaf size: 46
DSolve[y''''[x]-(3+I)*y'''[x]+(4+3*I)*y''[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (-\frac {3}{25}-\frac {4 i}{25}\right ) c_1 e^{(1+2 i) x}+\left (\frac {3}{25}+\frac {4 i}{25}\right ) c_2 e^{(2-i) x}+c_4 x+c_3 \]