28.2.26 problem 26

Internal problem ID [4469]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 26
Date solved : Monday, January 27, 2025 at 09:19:08 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\left (5\right )}+4 y^{\prime \prime \prime }&=7+x \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 39

dsolve(diff(y(x),x$5)+4*diff(y(x),x$3)=7+x,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x^{4}}{96}+\frac {7 x^{3}}{24}+\frac {c_3 \,x^{2}}{2}-\frac {c_{1} \sin \left (2 x \right )}{8}+\frac {c_{2} \cos \left (2 x \right )}{8}+c_4 x +c_5 \]

✓ Solution by Mathematica

Time used: 0.176 (sec). Leaf size: 52

DSolve[D[y[x],{x,5}]+4*D[y[x],{x,3}]==7+x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^4}{96}+\frac {7 x^3}{24}+c_5 x^2+c_4 x+\frac {1}{8} c_2 \cos (2 x)-\frac {1}{8} c_1 \sin (2 x)+c_3 \]