Internal problem ID [10561]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number: 4(b).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }-4 y^{\prime }+8 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$3)-2*diff(y(x),x$2)-4*diff(y(x),x)+8*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-2 x} c_{1} +c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{2 x} x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 27
DSolve[y'''[x]-2*y''[x]-4*y'[x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (e^{4 x} (c_3 x+c_2)+c_1\right ) \\ \end{align*}