Internal problem ID [9854]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1529.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _fully, _exact, _linear]]
\[ \boxed {\left (\sin \left (x \right )+x \right ) y^{\prime \prime \prime }+3 \left (1+\cos \left (x \right )\right ) y^{\prime \prime }-3 y^{\prime } \sin \left (x \right )-y \cos \left (x \right )=-\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve((sin(x)+x)*diff(diff(diff(y(x),x),x),x)+3*(cos(x)+1)*diff(diff(y(x),x),x)-3*diff(y(x),x)*sin(x)-y(x)*cos(x)+sin(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{3} +c_{1} x^{2}+x c_{2} -\cos \left (x \right )}{\sin \left (x \right )+x} \]
✓ Solution by Mathematica
Time used: 0.113 (sec). Leaf size: 28
DSolve[Sin[x] - Cos[x]*y[x] - 3*Sin[x]*y'[x] + 3*(1 + Cos[x])*y''[x] + (x + Sin[x])*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-\cos (x)+x (c_3 x+c_2)+c_1}{x+\sin (x)} \]