11.3 problem 3

Internal problem ID [12776]

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.
ODE order: 4.
ODE degree: 1.

CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]

\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y=3+\cos \left (2 x \right )} \]

✓ Solution by Maple

Time used: 0.016 (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)
 

\[ y \left (x \right ) = 3+\frac {\cos \left (2 x \right )}{9}+\left (c_{4} x +c_{1} \right ) \cos \left (x \right )+\left (c_{3} x +c_{2} \right ) \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.199 (sec). Leaf size: 36

DSolve[y''''[x]+2*y''[x]+y[x]==3+Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(x)\to \frac {1}{9} \cos (2 x)+(c_2 x+c_1) \cos (x)+c_3 \sin (x)+c_4 x \sin (x)+3 \]