Find the general equation of the following differential equations:

xy' + (1 + 2x^2)y = x3e-x^2

xy' +2y = (2/x^2) + 1

y' + 4y/(x-1) = 1/(x-1)5 + sinx/(x-1)4

Aresearch company wants to test the claim that a new multivitamin to improve short term memory. state the objective of the experiment, suggest a population, determine the experimental and control groups, and describe a sample procedure.

Which approach to the theory-and-research cycle does the following sequence reflect: (1) specific observations suggest generalizations, (2) generalizations produce a tentative theory, (3) the theory is tested through the formation of hypotheses, and (4) hypotheses may provide suggestions for additional observations?

Jamie went to home depot. she bought 25 bags of soil that cost $9 per bag. she bought 15 pots at $8 each, and she bought 23 bags of pebbles at $15 each. she used a coupon that gave her $5 off for every 100 dollars she spent. how much did jame pay at the end?