Internal problem ID [9869]
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]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y=32 \sin \left (2 x \right )-24 \cos \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
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)
\[ y \left (x \right ) = {\mathrm e}^{-2 x} \left (\left (c_{3} x +c_{1} \right ) {\mathrm e}^{3 x}+c_{4} x +\sin \left (2 x \right ) {\mathrm e}^{2 x}+c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 40
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]
\[ y(x)\to \sin (2 x)+e^{-2 x} \left (c_2 x+c_3 e^{3 x}+c_4 e^{3 x} x+c_1\right ) \]