28.2.18 problem 18

Internal problem ID [4461]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 18
Date solved : Monday, January 27, 2025 at 09:19:02 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=\sin \left (x \right )+x \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

dsolve(diff(y(x),x$3)+diff(y(x),x)=sin(x)+x*cos(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (-x^{2}-4 c_{2} +2\right ) \cos \left (x \right )}{4}+\frac {\left (x +4 c_{1} \right ) \sin \left (x \right )}{4}+c_3 \]

✓ Solution by Mathematica

Time used: 0.186 (sec). Leaf size: 36

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

\[ y(x)\to -\frac {1}{8} \left (2 x^2-3+8 c_2\right ) \cos (x)+\left (\frac {x}{4}+c_1\right ) \sin (x)+c_3 \]