Internal problem ID [2241]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime }=x \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$3)-diff(y(x),x)=x*sin(x),y(x), singsol=all)
\[ y = \frac {x \cos \left (x \right )}{2}-\sin \left (x \right )+c_{1} {\mathrm e}^{x}-{\mathrm e}^{-x} c_{2} +c_{3} \]
✓ Solution by Mathematica
Time used: 0.142 (sec). Leaf size: 34
DSolve[y'''[x]-y'[x]==x*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\sin (x)+\frac {1}{2} x \cos (x)+c_1 e^x-c_2 e^{-x}+c_3 \]