Internal problem ID [10232]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 43. Page
92
Problem number: Ex 4.
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 }-y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x$3)-2*diff(y(x),x$2)-diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 28
DSolve[y'''[x]-2*y''[x]-y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-x}+c_2 e^x+c_3 e^{2 x} \\ \end{align*}