Internal problem ID [13797]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 24. Variation of parameters. Additional exercises page 444
Problem number: 24.4 (c).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-81 y=\sinh \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 53
dsolve(diff(y(x),x$4)-81*y(x)=sinh(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (160 c_{3} {\mathrm e}^{6 x}+160 c_{1} \cos \left (3 x \right ) {\mathrm e}^{3 x}+160 c_{4} \sin \left (3 x \right ) {\mathrm e}^{3 x}-{\mathrm e}^{4 x}+{\mathrm e}^{2 x}+160 c_{2} \right ) {\mathrm e}^{-3 x}}{160} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 52
DSolve[y''''[x]-81*y[x]==Sinh[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-x}}{160}-\frac {e^x}{160}+c_1 e^{3 x}+c_3 e^{-3 x}+c_2 \cos (3 x)+c_4 \sin (3 x) \]