7.11.27 problem 27

Internal problem ID [348]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 27
Date solved : Wednesday, February 05, 2025 at 03:24:17 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=\sin \left (x \right )+\cos \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 50

dsolve(diff(y(x),x$4)+5*diff(y(x),x$2)+4*y(x)=sin(x)+cos(2*x),y(x), singsol=all)
 

\[ y = \frac {1}{9}+\frac {2 \left (-1+9 c_3 \right ) \cos \left (x \right )^{2}}{9}+\frac {\left (\left (-x +12 c_4 \right ) \sin \left (x \right )-x +6 c_1 \right ) \cos \left (x \right )}{6}+\frac {\left (18 c_2 +1\right ) \sin \left (x \right )}{18}-c_3 \]

✓ Solution by Mathematica

Time used: 0.108 (sec). Leaf size: 50

DSolve[D[y[x],{x,4}]+5*D[y[x],{x,2}]+4*y[x]==Sin[x]+Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (-\frac {11}{72}+c_1\right ) \cos (2 x)+\frac {1}{9} (-1+9 c_4) \sin (x)-\frac {1}{6} \cos (x) (x+(x-12 c_2) \sin (x)-6 c_3) \]