50.10.15 problem 4(b)

Internal problem ID [7984]
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)
Date solved : Monday, January 27, 2025 at 03:35:29 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.067 (sec). Leaf size: 31

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

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