Internal problem ID [624]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.3 Complex Roots of the Characteristic Equation ,
page 164
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+6 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 25
dsolve(diff(y(x),x$2) -2*diff(y(x),x)+6*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x} \sin \left (\sqrt {5}\, x \right )+c_{2} {\mathrm e}^{x} \cos \left (\sqrt {5}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 32
DSolve[y''[x]-2*y'[x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x \left (c_2 \cos \left (\sqrt {5} x\right )+c_1 \sin \left (\sqrt {5} x\right )\right ) \\ \end{align*}