The indicated functions are known linearly independent solutions of the associated homogeneous differential equation on (0, [infinity]). Find the general solution of the given nonhomogeneous equation. x2y'' + xy' + x2 − 1 4 y = x3/2; y1 = x−1/2 cos(x), y2 = x−1/2 sin(x)

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. (a) what is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips, inclusive? (b) what is the probability that a randomly selected bag contains fewer than 1125 chocolate chips? (c) what proportion of bags contains more than 1225 chocolate chips? (d) what is the percentile rank of a bag that contains 1425 chocolate chips?

He mass of a single atom of carbon can be found by dividing the atomic mass (12.01 g) by 6.022 x 10^23. which is the mass of a single carbon atom, correctly written in scientific notation with the correct number of significant figures?

Find the value of x in each case. give reasons to justify your solutions! d q ∈ pr