87.11.6 problem 6

Internal problem ID [23424]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 84
Problem number : 6
Date solved : Thursday, October 02, 2025 at 09:41:37 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 6 y^{\prime \prime \prime }-4 i y^{\prime \prime }+\left (3+i\right ) y^{\prime }-2 y&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 165

ode:=6*diff(diff(diff(y(x),x),x),x)-4*I*diff(diff(y(x),x),x)+(3+I)*diff(y(x),x)-2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\frac {2 i x}{9}} \left (c_1 \,{\mathrm e}^{-\frac {x \left (i \sqrt {3}\, \left (1080-388 i+36 \sqrt {996-447 i}\right )^{{2}/{3}}+70 i \sqrt {3}+\left (1080-388 i+36 \sqrt {996-447 i}\right )^{{2}/{3}}-18 \sqrt {3}-70-18 i\right )}{36 \left (1080-388 i+36 \sqrt {996-447 i}\right )^{{1}/{3}}}}+c_2 \,{\mathrm e}^{\frac {x \left (\left (i \sqrt {3}-1\right ) \left (1080-388 i+36 \sqrt {996-447 i}\right )^{{2}/{3}}+70+18 i+\left (-18+70 i\right ) \sqrt {3}\right )}{36 \left (1080-388 i+36 \sqrt {996-447 i}\right )^{{1}/{3}}}}+c_3 \,{\mathrm e}^{\frac {x \left (\left (1080-388 i+36 \sqrt {996-447 i}\right )^{{2}/{3}}-70-18 i\right )}{18 \left (1080-388 i+36 \sqrt {996-447 i}\right )^{{1}/{3}}}}\right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 141

ode=6*D[y[x],{x,3}]-4*I*D[y[x],{x,2}]+(3+I)*D[y[x],{x,1}]-2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_3 \exp \left (x \text {Root}\left [\left \{\text {$\#$1}^2+1\&,-4 \text {$\#$1} \text {$\#$2}^2+\text {$\#$1} \text {$\#$2}+6 \text {$\#$2}^3+3 \text {$\#$2}-2\&\right \},\{2,3\}\right ]\right )+c_2 \exp \left (x \text {Root}\left [\left \{\text {$\#$1}^2+1\&,-4 \text {$\#$1} \text {$\#$2}^2+\text {$\#$1} \text {$\#$2}+6 \text {$\#$2}^3+3 \text {$\#$2}-2\&\right \},\{2,2\}\right ]\right )+c_1 \exp \left (x \text {Root}\left [\left \{\text {$\#$1}^2+1\&,-4 \text {$\#$1} \text {$\#$2}^2+\text {$\#$1} \text {$\#$2}+6 \text {$\#$2}^3+3 \text {$\#$2}-2\&\right \},\{2,1\}\right ]\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*y(x) + (3 + I)*Derivative(y(x), x) - 4*I*Derivative(y(x), (x, 2)) + 6*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

RecursionError : maximum recursion depth exceeded