Internal problem ID [3262]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 4. Linear Differential Equations. Page 183
Problem number: 21.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime }=7 x -3 \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
dsolve(diff(y(x),x$4)+2*diff(y(x),x$2)=7*x-3*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {7 x^{3}}{12}-\frac {\cos \left (\sqrt {2}\, x \right ) c_{1}}{2}-\frac {c_{2} \sin \left (\sqrt {2}\, x \right )}{2}+3 \cos \left (x \right )+c_{3} x +c_{4} \]
✓ Solution by Mathematica
Time used: 0.603 (sec). Leaf size: 51
DSolve[y''''[x]+2*y''[x]==7*x-3*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {7 x^3}{12}+3 \cos (x)+c_4 x-\frac {1}{2} c_1 \cos \left (\sqrt {2} x\right )-\frac {1}{2} c_2 \sin \left (\sqrt {2} x\right )+c_3 \]