Internal problem ID [9127]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1548.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+11 y^{\prime \prime }-3 y^{\prime }-4 \cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (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)
\[ y \relax (x ) = {\mathrm e}^{x} c_{1}+2 c_{2} {\mathrm e}^{\frac {x}{2}}+\frac {2 c_{3} {\mathrm e}^{\frac {3 x}{2}}}{3}+\frac {18 \sin \relax (x )}{65}-\frac {14 \cos \relax (x )}{65}+c_{4} \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 50
DSolve[-4*Cos[x] - 3*y'[x] + 11*y''[x] - 12*Derivative[3][y][x] + 4*Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {18 \sin (x)}{65}-\frac {14 \cos (x)}{65}+2 c_1 e^{x/2}+\frac {2}{3} c_2 e^{3 x/2}+c_3 e^x+c_4 \\ \end{align*}