Internal problem ID [9047]
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]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime } \sin \left (x \right )-2 y^{\prime } \cos \left (x \right )+y \sin \left (x \right )-\ln \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
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)
\[ y \left (x \right ) = \left (c_{3} +\int \left (2 x c_{1} +c_{2} -\frac {3 x^{2}}{4}+\frac {\ln \left (x \right ) x^{2}}{2}\right ) {\mathrm e}^{\cos \left (x \right )}d x \right ) {\mathrm e}^{-\cos \left (x \right )} \]
✓ Solution by Mathematica
Time used: 2.399 (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]
\begin{align*} 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 ) \\ \end{align*}