Internal problem ID [303]
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 31.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }-8 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 29
dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)+4*diff(y(x),x)-8*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x} c_{1}+c_{2} {\mathrm e}^{-2 x} \sin \left (2 x \right )+c_{3} {\mathrm e}^{-2 x} \cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 33
DSolve[y'''[x]+3*y''[x]+4*y'[x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_3 e^x+e^{-2 x} (c_2 \cos (2 x)+c_1 \sin (2 x)) \\ \end{align*}