Internal problem ID [1554]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined
Coefficients for Higher Order Equations. Page 495
Problem number: section 9.3, problem 57.
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 }+4 y-\sinh \relax (x ) \cos \relax (x )+\cosh \relax (x ) \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.024 (sec). Leaf size: 73
dsolve(diff(y(x),x$4)+0*diff(y(x),x$3)-0*diff(y(x),x$2)-0*diff(y(x),x)+4*y(x)=sinh(x)*cos(x)-cosh(x)*sin(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {3 \,{\mathrm e}^{-x} \left ({\mathrm e}^{2 x}-1\right ) \cos \relax (x )}{64}+\frac {{\mathrm e}^{-x} \left (4 \,{\mathrm e}^{2 x} x -3 \,{\mathrm e}^{2 x}-4 x -3\right ) \sin \relax (x )}{64}+\cos \relax (x ) {\mathrm e}^{x} c_{1}+\sin \relax (x ) {\mathrm e}^{x} c_{2}+c_{3} \cos \relax (x ) {\mathrm e}^{-x}+c_{4} \sin \relax (x ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.355 (sec). Leaf size: 63
DSolve[y''''[x]+0*y'''[x]-0*y''[x]-0*y'[x]+4*y[x]==Sinh[x]*Cos[x]-Cosh[x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{64} e^{-x} \left (\left ((3+64 c_4) e^{2 x}-3+64 c_1\right ) \cos (x)+\left (-4 x+e^{2 x} (4 x-3+64 c_3)-3+64 c_2\right ) \sin (x)\right ) \\ \end{align*}