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.
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.