Differential Calculus

The topic is chemical reaction rate.

Two substances A and B are combined to form a product C. The formation of product is proportional to the time the reactants are combined. The final product is composed of three parts of A for every part of B. If initially A is 50 lbs and B is 60 lbs, and 10 lbs of the product is formed after 45 mins., find the time it takes for the reaction to form 25 lbs.

The answer is 135 minutes. Show complete solution please. Thank you.

1. y(x^2+xy-2y^2)dx+x(3y^2-xy-x^2)dy=0
2. (x+ysin y/x)dx-xsin y/x dy=0

v((2v^2) u -3) du + (3u^2) (v^2) - 3u + 4v) dv = 0

y' = (x + xy^2)/4y

ydx = {(e^ (3x) + 1)} dy

The topic is Population Growth, Decay and Investment. Somebody show the comple solution please.

A city has been found to have a population that triples every four years. If the city's population is one million in 2010, how many people were there in 1990?

The answer is 4,116.

the rod is 10ft long weighing 20lbs. if it revolves through one end at 2rps, find the total energy.

How can i solve this problem y' = 2(3x+y)²-1 when x = 0, y =0. Can someone show me the solution ?

(3 + y + 2y^2 sin ^ 2 ( x) ) dx + ( x + 2xy - y sin 2x) dy = 0

(xy^2 + x - 2y + 3) dx + x^2 ydy = 2(x+y) dy