Thread: Calculus Integration problem. NO clue

Question is as follows :

Let f be the function satisfying f ' (x) = -3xf(x) for all real numbers x, with f(1) = 4 and lim as x -> infinity of f(x) = 0.

a.) Evaluate the integral of -3xf(x) dx with bounds 1 and infinity.

b.) Use Euler's method, starting at x = 1 with a step size of .5 to approximate f(2)

c.) Write an expression for y = f(x) by solving the differential equation dy/dx = -3xy with the initial condition f(1) = 4


I dont really need help with b, once I figure out the equation I can do that one. But A and C have me completely stumped.

Originally Posted by Naveed103

Question is as follows :

Let f be the function satisfying f ' (x) = -3xf(x) for all real numbers x, with f(1) = 4 and lim as x -> infinity of f(x) = 0.

a.) Evaluate the integral of -3xf(x) dx with bounds 1 and infinity.

b.) Use Euler's method, starting at x = 1 with a step size of .5 to approximate f(2)

c.) Write an expression for y = f(x) by solving the differential equation dy/dx = -3xy with the initial condition f(1) = 4


I dont really need help with b, once I figure out the equation I can do that one. But A and C have me completely stumped.

a.) Integrate both sides of f ' (x) = -3xf(x): .

Therefore .

c.) dy/dx = -3xy is seperable: etc. etc.

thanks a lot for your help on a. So if I integrate c, I get y/4 = -3/2 x^2 + c. f(1) = 4, and c = 10, so the final solution is y/4 = -3/2 x^2 + 5/2 or y = -6x^2 + 10?

Originally Posted by Naveed103

thanks a lot for your help on a. So if I integrate c, I get y/4 = -3/2 x^2 + c. f(1) = 4, and c = 10, so the final solution is y/4 = -3/2 x^2 + 5/2 or y = -6x^2 + 10?

First of all, you can check a solution by substituting it back into the DE. Does your answer work?

I cannot see how you could possibly figure that the integral of 1/y is y/4, which I guess preempts the answer to my question above .......

oh I'm sorry. The 1/y I wrote on my paper looks like 1/4, ><. I've got bad handwriting and it's late. so if you integrate 1/y you get lny = -3/2 x^2 + c. If I solve for c I get 2.88, which seems like a really odd number. I'm sorry if these questions are stupid, I'm not very good at this stuff.