60.4.1 problem 1449

Internal problem ID [11424]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1449
Date solved : Sunday, March 30, 2025 at 08:21:59 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-\lambda y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 45

ode:=diff(diff(diff(y(x),x),x),x)-lambda*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-\frac {\lambda ^{{1}/{3}} \left (1+i \sqrt {3}\right ) x}{2}}+c_2 \,{\mathrm e}^{\frac {\lambda ^{{1}/{3}} \left (i \sqrt {3}-1\right ) x}{2}}+c_3 \,{\mathrm e}^{\lambda ^{{1}/{3}} x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 53

ode=-(\[Lambda]*y[x]) + Derivative[3][y][x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 e^{(-1)^{2/3} \sqrt [3]{\lambda } x}+c_2 e^{-\sqrt [3]{-1} \sqrt [3]{\lambda } x}+c_3 e^{\sqrt [3]{\lambda } x} \]

✓ Sympy. Time used: 0.147 (sec). Leaf size: 53

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

\[ y{\left (x \right )} = C_{1} e^{\sqrt [3]{\lambda _{}} x} + C_{2} e^{\frac {\sqrt [3]{\lambda _{}} x \left (-1 + \sqrt {3} i\right )}{2}} + C_{3} e^{- \frac {\sqrt [3]{\lambda _{}} x \left (1 + \sqrt {3} i\right )}{2}} \]