Internal problem ID [3259]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 4. Linear Differential Equations. Page 183
Problem number: 18.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime }=\sin \left (x \right )+\cos \left (x \right ) x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$3)+diff(y(x),x)=sin(x)+x*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\cos \left (x \right ) x^{2}}{4}+\frac {\cos \left (x \right )}{2}+\frac {x \sin \left (x \right )}{4}-c_{2} \cos \left (x \right )+\sin \left (x \right ) c_{1} +c_{3} \]
✓ Solution by Mathematica
Time used: 0.237 (sec). Leaf size: 36
DSolve[y'''[x]+y'[x]==Sin[x]+x*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{8} \left (2 x^2-3+8 c_2\right ) \cos (x)+\left (\frac {x}{4}+c_1\right ) \sin (x)+c_3 \]