60.5.2 problem 1535

Internal problem ID [11499]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1535
Date solved : Sunday, March 30, 2025 at 08:23:42 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y-f&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 36

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

\[ y = \frac {f}{4}+c_1 \,{\mathrm e}^{x} \cos \left (x \right )+c_2 \,{\mathrm e}^{x} \sin \left (x \right )+c_3 \,{\mathrm e}^{-x} \cos \left (x \right )+c_4 \,{\mathrm e}^{-x} \sin \left (x \right ) \]

✓ Mathematica. Time used: 0.161 (sec). Leaf size: 172

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

\[ y(x)\to e^{-x} \left (\cos (x) \int _1^x\frac {1}{8} e^{K[1]} f(K[1]) (\cos (K[1])-\sin (K[1]))dK[1]+e^{2 x} \cos (x) \int _1^x-\frac {1}{8} e^{-K[4]} f(K[4]) (\cos (K[4])+\sin (K[4]))dK[4]+\sin (x) \int _1^x\frac {1}{8} e^{K[2]} f(K[2]) (\cos (K[2])+\sin (K[2]))dK[2]+e^{2 x} \sin (x) \int _1^x\frac {1}{8} e^{-K[3]} f(K[3]) (\cos (K[3])-\sin (K[3]))dK[3]+c_1 \cos (x)+c_4 e^{2 x} \cos (x)+c_2 \sin (x)+c_3 e^{2 x} \sin (x)\right ) \]

✓ Sympy. Time used: 0.118 (sec). Leaf size: 32

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

\[ y{\left (x \right )} = \frac {f}{4} + \left (C_{1} \sin {\left (x \right )} + C_{2} \cos {\left (x \right )}\right ) e^{- x} + \left (C_{3} \sin {\left (x \right )} + C_{4} \cos {\left (x \right )}\right ) e^{x} \]