12.19.57 problem section 9.3, problem 57

Internal problem ID [2204]
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
Date solved : Monday, January 27, 2025 at 05:43:31 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y&=\sinh \left (x \right ) \cos \left (x \right )-\cosh \left (x \right ) \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.211 (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)
 

\[ y = \frac {\left (\left (-4 x +64 c_4 -3\right ) \sin \left (x \right )+\cos \left (x \right ) \left (64 c_3 -3\right )\right ) {\mathrm e}^{-x}}{64}+\frac {\left (\left (x +16 c_2 -\frac {3}{4}\right ) \sin \left (x \right )+\cos \left (x \right ) \left (16 c_1 +\frac {3}{4}\right )\right ) {\mathrm e}^{x}}{16} \]

✓ Solution by Mathematica

Time used: 0.558 (sec). Leaf size: 63

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

\[ y(x)\to \frac {1}{64} e^{-x} \left (\left ((3+64 c_4) e^{2 x}-3+64 c_1\right ) \cos (x)+\left (-4 x+e^{2 x} (4 x-3+64 c_3)-3+64 c_2\right ) \sin (x)\right ) \]