Briefly describe the following:
(a) Transcription
(b) Polymorphism
(c) Translation
(d) Bioinformatics
Prove that \(x^2-y^2=c(x^2+y^2)\)is the general solution of differential equation(\(x^3-3xy^2)dx=(y^3-3x^2y)dy\),where \(c\) is parameter.
Show that the points \(A(1,2,7),B(2,6,3)\),and \(C(3,10,-1)\) are collinear.
Suppose that two cards are drawn at random from a deck of cards. Let X be the number of aces obtained. What is the value of E(X)?
For each of the exercises given below, verify that the given function (implicit or explicit)is a solution of the corresponding differential equation.
i) \(y=ae^x+be^{-x}+x^2: x\frac{d^2y}{dx^2}+2\frac{dy}{dx}-xy+x^2-2=0\)
ii) \(y=e^x(a \cos x+ b \sin x):\frac{d^2y}{dx^2}-2\frac{dy}{dx}+2y=0\)
iii) \(y= x \sin 3x:\frac{d^2y}{dx^2}+9y-6\cos3x=0\)
iv) \(x^2=2y^2\log y:(x^2+y^2)\frac{dy}{dx}-xy=0\)