Question

!!Urgent help needed!! Find an explicit solution of the given initial-value problem. (x^2)(dy/dx) = y-xy, y(-1) = -1

Answer 1

@e.mccormick Do you think you could help me really quick?

Answer 2

I have the answer, Im just lost in the steps. A quick walkthrough is all i need.

Answer 3

you may solve this by 'separating variables'

Answer 4

(x^2)(dy/dx) = y-xy

(x^2)(dy/dx) = y(1-x)

Answer 5

I got that part, i dont know how to solve for c

Answer 6

solving c is easy, you just need to plugin the point (-1, -1) in general solution.
wats the general solution u got ?

Answer 7

C=-e^(-2)

Answer 8

im asking about general solution..

Answer 9

thats where im stuck. I got y=ce^(-1/x-x)

Answer 10

dx(1-x)/x^2 = dy/y

x^-2 - 1/x dx = 1/y dy

-1/x - ln |x| = ln |y| + C

ln |xy| = -1/x + c

xy = e^(-1/x+c)

y = e^(-1/x+c)/x

Answer 11

^^ i am getting that, next rewrite constant e^c as A

Answer 12

y = e^(-1/x+c)/x

y = Ae^(-1/x)/x

plugin the point (-1, -1) and solve A

Answer 13

y = Ae^(-1/x)/x


-1 = Ae^(-1/-1) / -1

1 = Ae

A = 1/e

Answer 14

book says: y = (e^-(1+1/x))/x

Answer 15

yes thats correct

Answer 16

y = Ae^(-1/x)/x


plugin A = 1/e and simplify