Solve dy/dx=1+1/y^2 ?

sombereki51 2022-09-26 Answered
Solve d y d x = 1 + 1 y 2 ?
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Answers (1)

June Rowland
Answered 2022-09-27 Author has 6 answers
We have:
d y d x = 1 + 1 y 2
Which is a First Order Separable Ordinary Differential Equation so we can rearrange and "separate the variables":
d y d x = 1 + y 2 y 2
  y 2 1 + y 2   d y =   d x
We can manipulate the LHS integral:
            1 + y 2 - 1 1 + y 2   d y =   d x
  1 - 1 1 + y 2   d y =   d x
Which is now trivial to integrate giving us:
y - arctan ( y ) = x + C
Which is the general implicit solution.
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