60.5.11 problem 1548

Internal problem ID [11508]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1548
Date solved : Wednesday, March 05, 2025 at 02:27:10 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} 4 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+11 y^{\prime \prime }-3 y^{\prime }-4 \cos \left (x \right )&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 32

ode:=4*diff(diff(diff(diff(y(x),x),x),x),x)-12*diff(diff(diff(y(x),x),x),x)+11*diff(diff(y(x),x),x)-3*diff(y(x),x)-4*cos(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 2 c_{2} {\mathrm e}^{\frac {x}{2}}+\frac {2 c_3 \,{\mathrm e}^{\frac {3 x}{2}}}{3}+{\mathrm e}^{x} c_{1} +\frac {18 \sin \left (x \right )}{65}-\frac {14 \cos \left (x \right )}{65}+c_4 \]

✓ Mathematica. Time used: 0.074 (sec). Leaf size: 120

ode=-4*Cos[x] - 3*D[y[x],x] + 11*D[y[x],{x,2}] - 12*Derivative[3][y][x] + 4*Derivative[4][y][x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.257 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*cos(x) - 3*Derivative(y(x), x) + 11*Derivative(y(x), (x, 2)) - 12*Derivative(y(x), (x, 3)) + 4*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{\frac {x}{2}} + C_{3} e^{x} + C_{4} e^{\frac {3 x}{2}} + \frac {18 \sin {\left (x \right )}}{65} - \frac {14 \cos {\left (x \right )}}{65} \]