Solving Diff. Eq. to Find Solutions (1, 0)

[johann1301h]

Homework Statement

[/B]
Solve the differenetial equation and find the all solutions through (1, 0).
y'/y^2 = 1

The Attempt at a Solution

i find one solution: 1/(1-x). But the math book says 1/(1-2x) also is a solution. How do i find this solution?

I used that ∫y^-2dy = ∫1dx to find the first solution.

 

[Ray Vickson]

Homework Statement

[/B]
Solve the differenetial equation and find the all solutions through (1, 0).
y'/y^2 = 1

The Attempt at a Solution

i find one solution: 1/(1-x). But the math book says 1/(1-2x) also is a solution. How do i find this solution?

I used that ∫y^-2dy = ∫1dx to find the first solution.

You need to show the actual details of your solution in order for us to see where you went wrong.

 

[ehild]

i find one solution: 1/(1-x). But the math book says 1/(1-2x) also is a solution.

Is it really a solution? Replace it back into the original equation.

 

[vela]

Homework Statement

[/B]
Solve the differenetial equation and find the all solutions through (1, 0).
y'/y^2 = 1

A solution where $y=0$ at some point? Isn't that a problem with the given differential equation?