The discussion revolves around solving the differential equation y'/y^2 = 1 and finding all solutions that pass through the point (1, 0). Participants are exploring the validity of different solutions presented in a math book.
The discussion is active, with participants seeking clarification on the solutions and their validity. Some have requested more details on the solution process to identify potential errors, while others are questioning the implications of having a solution where y=0 at some point.
There is a concern regarding the behavior of the solutions in relation to the differential equation, particularly when y approaches zero, which may affect the validity of the solutions being discussed.
johann1301h said:Homework Statement
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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.
Is it really a solution? Replace it back into the original equation.johann1301h said:i find one solution: 1/(1-x). But the math book says 1/(1-2x) also is a solution.
A solution where ##y=0## at some point? Isn't that a problem with the given differential equation?johann1301h said:Homework Statement
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Solve the differenetial equation and find the all solutions through (1, 0).
y'/y^2 = 1