Internal problem ID [4068]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number: Exercise 20.7, page 220.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }-6 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(x),x$3)+diff(y(x),x$2)-10*diff(y(x),x)-6*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{3 x} c_{1} +c_{2} {\mathrm e}^{\left (-2+\sqrt {2}\right ) x}+c_{3} {\mathrm e}^{-\left (2+\sqrt {2}\right ) x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 43
DSolve[y'''[x]+y''[x]-10*y'[x]-6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-\left (\left (2+\sqrt {2}\right ) x\right )}+c_2 e^{\left (\sqrt {2}-2\right ) x}+c_3 e^{3 x} \\ \end{align*}