Internal problem ID [9797]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1470.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _fully, _exact, _linear]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime } \sin \left (x \right )-2 \cos \left (x \right ) y^{\prime }+y \sin \left (x \right )=\ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve(diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x)*sin(x)-2*diff(y(x),x)*cos(x)+y(x)*sin(x)-ln(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (4 c_{3} +\int \left (8 c_{1} x +4 c_{2} -3 x^{2}+2 x^{2} \ln \left (x \right )\right ) {\mathrm e}^{\cos \left (x \right )}d x \right ) {\mathrm e}^{-\cos \left (x \right )}}{4} \]
✓ Solution by Mathematica
Time used: 2.289 (sec). Leaf size: 57
DSolve[-Log[x] + Sin[x]*y[x] - 2*Cos[x]*y'[x] - Sin[x]*y''[x] + Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-\cos (x)} \left (\int _1^x\frac {1}{4} e^{\cos (K[1])} \left (2 \log (K[1]) K[1]^2-3 K[1]^2+4 c_1 K[1]+4 c_2\right )dK[1]+c_3\right ) \]