I need answers for numer 1, 2, 3, 6, and 7 Draw a direction field for the differ

Question

I need answers for numer

1, 2, 3, 6, and 7

Draw a direction field for the differential equation. Determine the behavior of y as t rightarrow infinity. dy/dx = 2 -y Determine the order of the differential equation. Also, state whether the equation is linear or nonlinear. t2 d2y/dt2 + 3t dt/dt - 5y = cos(t) d2y/dt2 - 2 sing(y) = 1 Verify that the given function is a solution of the differential equation. y"-4y = 0 , y = 3e 2t State where in the ty-plane for the given differential equation would, by the existence and uniqueness theorem, have a unique solution whose graph passes through a point (x 0, y) in the region. DO NOT SOLVE, dy/dx = (y + 1)1/3 Consider a population of field mice that grows at a rate proportional to the current population, so that dp/dt = rp. Find the growth rate r if the population doubles in 60 days. Solve the exact DE. 4xydx + 2x 2dy = 0 Solve the initial value problem of the given linear differential equation and initial value. Give the largest interval I over which the general solution is defined. y' + 2y/x = sin(x) , y(0) = 2

Explanation / Answer

so we have to solve all of them

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