28.2.21 problem 21

Internal problem ID [4464]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 21
Date solved : Monday, January 27, 2025 at 09:19:05 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }&=7 x -3 \cos \left (x \right ) \end{align*}

✓ 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)
 

\[ y \left (x \right ) = \frac {7 x^{3}}{12}-\frac {\cos \left (\sqrt {2}\, x \right ) c_{1}}{2}-\frac {c_{2} \sin \left (\sqrt {2}\, x \right )}{2}+3 \cos \left (x \right )+x c_3 +c_4 \]

✓ Solution by Mathematica

Time used: 0.572 (sec). Leaf size: 51

DSolve[D[y[x],{x,4}]+2*D[y[x],{x,2}]==7*x-3*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {7 x^3}{12}+3 \cos (x)+c_4 x-\frac {1}{2} c_1 \cos \left (\sqrt {2} x\right )-\frac {1}{2} c_2 \sin \left (\sqrt {2} x\right )+c_3 \]