60.5.3 problem 1536

Internal problem ID [11500]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1536
Date solved : Sunday, March 30, 2025 at 08:23:43 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 48

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

\[ y = c_1 \,{\mathrm e}^{-i \left (-\lambda \right )^{{1}/{4}} x}+c_2 \,{\mathrm e}^{i \left (-\lambda \right )^{{1}/{4}} x}+c_3 \,{\mathrm e}^{-\left (-\lambda \right )^{{1}/{4}} x}+c_4 \,{\mathrm e}^{\left (-\lambda \right )^{{1}/{4}} x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 76

ode=\[Lambda]*y[x] + Derivative[4][y][x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 e^{(-1)^{3/4} \sqrt [4]{\lambda } x}+c_2 e^{-\sqrt [4]{-1} \sqrt [4]{\lambda } x}+c_3 e^{-(-1)^{3/4} \sqrt [4]{\lambda } x}+c_4 e^{\sqrt [4]{-1} \sqrt [4]{\lambda } x} \]

✓ Sympy. Time used: 0.152 (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, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x \sqrt [4]{- \lambda _{}}} + C_{2} e^{x \sqrt [4]{- \lambda _{}}} + C_{3} e^{- i x \sqrt [4]{- \lambda _{}}} + C_{4} e^{i x \sqrt [4]{- \lambda _{}}} \]