60.5.9 problem 1545

Internal problem ID [11506]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1545
Date solved : Sunday, March 30, 2025 at 08:23:50 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y-32 \sin \left (2 x \right )+24 \cos \left (2 x \right )&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 33

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+2*diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x)-4*diff(y(x),x)+4*y(x)-32*sin(2*x)+24*cos(2*x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\left (c_3 x +c_1 \right ) {\mathrm e}^{3 x}+c_4 x +\sin \left (2 x \right ) {\mathrm e}^{2 x}+c_2 \right ) {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 40

ode=24*Cos[2*x] - 32*Sin[2*x] + 4*y[x] - 4*D[y[x],x] - 3*D[y[x],{x,2}] + 2*Derivative[3][y][x] + Derivative[4][y][x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \sin (2 x)+e^{-2 x} \left (c_2 x+c_3 e^{3 x}+c_4 e^{3 x} x+c_1\right ) \]

✓ Sympy. Time used: 0.324 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) - 32*sin(2*x) + 24*cos(2*x) - 4*Derivative(y(x), x) - 3*Derivative(y(x), (x, 2)) + 2*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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