60.5.11 problem 1545

Internal problem ID [11545]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 4, linear fourth order
Problem number : 1545
Date solved : Monday, January 27, 2025 at 11:23:21 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} 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{align*}

✓ Solution by Maple

Time used: 0.007 (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)
 

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

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 40

DSolve[24*Cos[2*x] - 32*Sin[2*x] + 4*y[x] - 4*D[y[x],x] - 3*D[y[x],{x,2}] + 2*Derivative[3][y][x] + Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sin (2 x)+e^{-2 x} \left (c_2 x+c_3 e^{3 x}+c_4 e^{3 x} x+c_1\right ) \]