7.11.12 problem 12

Internal problem ID [333]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 12
Date solved : Wednesday, February 05, 2025 at 03:21:03 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=2-\sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve(diff(y(x),x$3)+diff(y(x),x)=2-sin(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.159 (sec). Leaf size: 35

DSolve[D[y[x],{x,3}]+D[y[x],x]==2-Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

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