15.15.8 problem 9

Internal problem ID [3212]
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 : 9
Date solved : Monday, January 27, 2025 at 07:26:12 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=x \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)=x*sin(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.161 (sec). Leaf size: 34

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

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