Internal problem ID [2753]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime }-7 x +3 \cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (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)
\[ y \relax (x ) = \frac {7 x^{3}}{12}-\frac {\cos \left (x \sqrt {2}\right ) c_{1}}{2}-\frac {\sin \left (x \sqrt {2}\right ) c_{2}}{2}+3 \cos \relax (x )+c_{3} x +c_{4} \]
✓ Solution by Mathematica
Time used: 0.197 (sec). Leaf size: 51
DSolve[y''''[x]+2*y''[x]==7*x-3*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 \\ \end{align*}