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

sombereki51 2022-09-26 Answered
Solve $\frac{dy}{dx}=1+\frac{1}{{y}^{2}}$ ?
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## Answers (1)

June Rowland
Answered 2022-09-27 Author has 6 answers
We have:
$\frac{dy}{dx}=1+\frac{1}{{y}^{2}}$
Which is a First Order Separable Ordinary Differential Equation so we can rearrange and "separate the variables":
$\frac{dy}{dx}=\frac{1+{y}^{2}}{{y}^{2}}$

We can manipulate the LHS integral:

Which is now trivial to integrate giving us:
$y-\mathrm{arctan}\left(y\right)=x+C$
Which is the general implicit solution.
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