Internal problem ID [9863]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1538.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y=\cosh \left (x a \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 51
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+2*a^2*diff(diff(y(x),x),x)+a^4*y(x)-cosh(a*x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-a x}+\left (8 c_{3} x +8 c_{1} \right ) a^{4} \cos \left (a x \right )+\left (8 c_{4} x +8 c_{2} \right ) a^{4} \sin \left (a x \right )+{\mathrm e}^{a x}}{8 a^{4}} \]
✓ Solution by Mathematica
Time used: 0.185 (sec). Leaf size: 41
DSolve[-Cosh[a*x] + a^4*y[x] + 2*a^2*y''[x] + Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\cosh (a x)}{4 a^4}+(c_2 x+c_1) \cos (a x)+(c_4 x+c_3) \sin (a x) \]