Internal problem ID [12456]
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: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$4)+2*diff(y(x),x$2)+y(x)=3+cos(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\cos \left (2 x \right )}{9}+3+c_{1} \cos \left (x \right )+c_{2} \sin \left (x \right )+c_{3} x \cos \left (x \right )+c_{4} \sin \left (x \right ) x \]
✓ 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]
\[ y(x)\to \frac {1}{9} \cos (2 x)+(c_2 x+c_1) \cos (x)+c_3 \sin (x)+c_4 x \sin (x)+3 \]