Internal problem ID [831]
Book: Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima,
Meade
Section: Chapter 4.2, Higher order linear differential equations. Constant coefficients. page
180
Problem number: 17.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve(diff(y(x),x$3)+5*diff(y(x),x$2)+6*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{\left (\sqrt {2}-2\right ) x}+c_{3} {\mathrm e}^{-\left (2+\sqrt {2}\right ) x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 43
DSolve[y'''[x]+5*y''[x]+6*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \left (e^{-\left (\left (1+\sqrt {2}\right ) x\right )} \left (c_2 e^{2 \sqrt {2} x}+c_1\right )+c_3\right ) \\ \end{align*}