71.10.13 problem 18

Internal problem ID [14437]
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
Date solved : Monday, March 31, 2025 at 12:27:09 PM
CAS classification : [[_high_order, _missing_x]]

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

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

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-(3+I)*diff(diff(diff(y(x),x),x),x)+(4+3*I)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{\left (2-i\right ) x}+c_2 \,{\mathrm e}^{\left (1+2 i\right ) x}+c_3 +c_4 x \]

✓ Mathematica. Time used: 0.094 (sec). Leaf size: 46

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

\[ y(x)\to \left (-\frac {3}{25}-\frac {4 i}{25}\right ) c_1 e^{(1+2 i) x}+\left (\frac {3}{25}+\frac {4 i}{25}\right ) c_2 e^{(2-i) x}+c_4 x+c_3 \]

✓ Sympy. Time used: 0.136 (sec). Leaf size: 68

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(complex(-3, -1)*Derivative(y(x), (x, 3)) + complex(4, 3)*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} e^{\frac {x \left (\sqrt {\operatorname {complex}^{2}{\left (-3,-1 \right )} - 4 \operatorname {complex}{\left (4,3 \right )}} - \operatorname {complex}{\left (-3,-1 \right )}\right )}{2}} + C_{4} e^{- \frac {x \left (\sqrt {\operatorname {complex}^{2}{\left (-3,-1 \right )} - 4 \operatorname {complex}{\left (4,3 \right )}} + \operatorname {complex}{\left (-3,-1 \right )}\right )}{2}} \]