Show calculus steps for all problems and underline answers for all

Question

1) The quantity of a substance can be modeled by the function k(t) that satisfies the differential equation dk/ dt =-1/90 (k-450). One point on this function is k(2) = 900. Based on this model, use a linear approximation to the graph of k(t) at t = 2 to estimate the quantity of the substance at t = 2.1.

2) Consider the differential equation dy/dx =x^2y^2with a particular solution y=f(x) having an initial condition y(−3) = 1 . Use the equation of the line tangent to the graph of f at the point (−3, 1) in order to approximate the value of f(−2.8) .

3) Given the differential equation dy/dx=-x/y^2 find the particular solution, y=f(x) , with the initial condition f(−6) = −3 .

4) What is the particular solution to the differential equation dy/dx =3 cos(x)y with the initial condition y(pi/2)=-2?

Answer 1

You need to work these problems for yourself.

The variables are separable in all 4 questions...so the solution method is the same in each.

If you get stuck on a particular one, ask a specific question.

I will start the 2nd one for you:

dy/y² = x²dx

-1/y = (x³/3)+C

then figure C using the initial conditions.