Differential Equations Answers

Two runners start a race at the same time and finish in a tie. Prove that at some time during the race they have the same speed.

Find the relative extrema using both first and second

derivative tests. f(x) = sin 2x, 0 < x < π

ydx + (1-3y)xdy = 3y²e³ydy

In a series RL circuit, L = 4H, R = 100 ohms and E = 200V . Find the values of current as a function of time. Assume that the initial current is zero. Find the current when t = 2 secons.

An inductance of 1 henry and a resistance of 1 ohm are connected in series with a constant e.m.f. of E volts. If 10 A after 5 seconds, find E

An inductance of L Henrys and a resistance of 10 ohms are connected in series with e.m.f. of 100 volts. If the current is initially zero, and is equal to 9 amperes after 1 second , find L and find the current after 0.5 second

the curve y = f(x) has a y-intercept of 3. the tangent to this curve at the point (x, y) has an x-intercept of x+2. What is the equation of this curve?

Find a partial differential equation by eliminating a and b from the equations

z^2 = ax^3 + by^3 + ab.

Find a partial differential equation by eliminating a and b from the equations of

z = ax + (1 − a)y + b.