71.11.3 problem 3

Internal problem ID [14512]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.4, page 218
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 06:42:51 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y&=3+\cos \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 28

dsolve(diff(y(x),x$4)+2*diff(y(x),x$2)+y(x)=3+cos(2*x),y(x), singsol=all)
 

\[ y = 3+\frac {\cos \left (2 x \right )}{9}+\left (c_4 x +c_{1} \right ) \cos \left (x \right )+\left (c_{3} x +c_{2} \right ) \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.219 (sec). Leaf size: 135

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

\[ y(x)\to \sin (x) \int _1^x\frac {1}{2} (\cos (2 K[2])+3) (\cos (K[2])+K[2] \sin (K[2]))dK[2]+x \sin (x) \int _1^x-\frac {1}{2} (\cos (2 K[3])+3) \sin (K[3])dK[3]+\cos (x) \int _1^x\frac {1}{2} (\cos (2 K[1])+3) (\cos (K[1]) K[1]-\sin (K[1]))dK[1]+\frac {1}{3} x \sin ^3(x) \cos (x)-2 x \sin (x) \cos (x)+c_1 \cos (x)+c_2 x \cos (x)+c_3 \sin (x)+c_4 x \sin (x) \]