60.5.13 problem 1548

Internal problem ID [11547]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1548
Date solved : Monday, January 27, 2025 at 11:23:22 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*}

✓ Solution by Maple

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

dsolve(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,y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[-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,y[x],x,IncludeSingularSolutions -> True]
 

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