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]]
\[ \boxed {y^{\prime \prime \prime \prime }+4 y=\sinh \left (x \right ) \cos \left (x \right )-\cosh \left (x \right ) \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 53
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)
\[ y \left (x \right ) = \frac {\left (\left (-4 x +64 c_{4} -3\right ) \sin \left (x \right )+\cos \left (x \right ) \left (64 c_{3} -3\right )\right ) {\mathrm e}^{-x}}{64}+\frac {{\mathrm e}^{x} \left (\left (x +16 c_{2} -\frac {3}{4}\right ) \sin \left (x \right )+\cos \left (x \right ) \left (16 c_{1} +\frac {3}{4}\right )\right )}{16} \]
✓ Solution by Mathematica
Time used: 0.676 (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]
\[ y(x)\to \frac {1}{64} e^{-x} \left (\left ((3+64 c_4) e^{2 x}-3+64 c_1\right ) \cos (x)+\left (-4 x+e^{2 x} (4 x-3+64 c_3)-3+64 c_2\right ) \sin (x)\right ) \]