15.15.7 problem 8

Internal problem ID [3211]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 24, page 109
Problem number : 8
Date solved : Monday, January 27, 2025 at 07:26:11 AM
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: 0.001 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.071 (sec). Leaf size: 31

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

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