Internal problem ID [9043]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1464.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime }+10 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 27
dsolve(diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)-3*diff(y(x),x)+10*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-2 x}+c_{2} {\mathrm e}^{2 x} \sin \relax (x )+c_{3} {\mathrm e}^{2 x} \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 31
DSolve[10*y[x] - 3*y'[x] - 2*y''[x] + Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_3 e^{-2 x}+e^{2 x} (c_2 \cos (x)+c_1 \sin (x)) \\ \end{align*}