Internal problem ID [9124]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1545.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {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 {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 31
dsolve(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,y(x), singsol=all)
\[ y \relax (x ) = \sin \left (2 x \right )+{\mathrm e}^{x} c_{1}+c_{2} {\mathrm e}^{-2 x}+c_{3} x \,{\mathrm e}^{x}+c_{4} {\mathrm e}^{-2 x} x \]
✓ Solution by Mathematica
Time used: 0.26 (sec). Leaf size: 34
DSolve[24*Cos[2*x] - 32*Sin[2*x] + 4*y[x] - 4*y'[x] - 3*y''[x] + 2*Derivative[3][y][x] + Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sin (2 x)+e^{-2 x} (c_2 x+c_1)+e^x (c_4 x+c_3) \\ \end{align*}