Internal problem ID [5562]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.2. THE METHOD OF UNDETERMINED
COEFFICIENTS. Page 67
Problem number: 4(b).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime }-\sin \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$3)+diff(y(x),x)=sin(x),y(x), singsol=all)
\[ y \left (x \right ) = -\cos \left (x \right )-\frac {\sin \left (x \right ) x}{2}+c_{1} \sin \left (x \right )-c_{2} \cos \left (x \right )+c_{3} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 31
DSolve[y'''[x]+y'[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} (1+2 c_2) \cos (x)+\left (-\frac {x}{2}+c_1\right ) \sin (x)+c_3 \\ \end{align*}