Internal problem ID [301]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with
Constant Coefficients. Page 300
Problem number: problem 29.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+27 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(x),x$3)+27*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-3 x}+c_{2} {\mathrm e}^{\frac {3 x}{2}} \sin \left (\frac {3 \sqrt {3}\, x}{2}\right )+c_{3} {\mathrm e}^{\frac {3 x}{2}} \cos \left (\frac {3 \sqrt {3}\, x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 51
DSolve[y'''[x]+27*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-3 x}+e^{3 x/2} \left (c_3 \cos \left (\frac {3 \sqrt {3} x}{2}\right )+c_2 \sin \left (\frac {3 \sqrt {3} x}{2}\right )\right ) \\ \end{align*}