Internal problem ID [9108]
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]]
Solve \begin {gather*} \boxed {\left (\sin \relax (x )+x \right ) y^{\prime \prime \prime }+3 \left (\cos \relax (x )+1\right ) y^{\prime \prime }-3 y^{\prime } \sin \relax (x )-y \cos \relax (x )+\sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 43
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)
\[ y \relax (x ) = \frac {x^{2} c_{1}}{\sin \relax (x )+x}+\frac {c_{2} x}{\sin \relax (x )+x}-\frac {\cos \relax (x )}{\sin \relax (x )+x}+\frac {c_{3}}{\sin \relax (x )+x} \]
✓ Solution by Mathematica
Time used: 0.075 (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]
\begin{align*} y(x)\to \frac {-\cos (x)+x (c_3 x+c_2)+c_1}{x+\sin (x)} \\ \end{align*}