Internal problem ID [9853]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1528.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime } \sin \left (x \right )+\left (2 \cos \left (x \right )+1\right ) y^{\prime \prime }-y^{\prime } \sin \left (x \right )=\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 68
dsolve(diff(diff(diff(y(x),x),x),x)*sin(x)+(2*cos(x)+1)*diff(diff(y(x),x),x)-diff(y(x),x)*sin(x)-cos(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\ln \left (\csc \left (x \right )-\cot \left (x \right )\right ) c_{1} -\ln \left (\sin \left (x \right )\right ) c_{1} -\cot \left (x \right )^{2} x +\left (c_{1} x +c_{2} +1\right ) \cot \left (x \right )+\csc \left (x \right )^{2} x +\left (-c_{1} x -c_{2} -1\right ) \csc \left (x \right )-c_{3}}{-\csc \left (x \right )+\cot \left (x \right )} \]
✓ Solution by Mathematica
Time used: 4.252 (sec). Leaf size: 56
DSolve[-Cos[x] - Sin[x]*y'[x] + (1 + 2*Cos[x])*y''[x] + Sin[x]*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \cot \left (\frac {x}{2}\right ) \arcsin (\cos (x))-\frac {c_2 x}{\sqrt {2}}-\frac {\cot \left (\frac {x}{2}\right ) (c_2 \log (2 (\cos (x)+1))+2 c_1)}{\sqrt {2}}+c_3 \]