Internal problem ID [4287]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 5. SECOND-ORDER LINEAR
EQUATIONSWITH CONSTANT COEFFICIENTS AND ZERO RIGHT-HAND SIDE. page
414
Problem number: 5.
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: 0.0 (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: 0.005 (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*}