# What is a solution to the differential equation #dy/dx=-x/y# with the particular solution #y(1)=-sqrt2#?

Multiply both sides by

Because the form of C is arbitrary, we can write the above as our friend the circle:

Forcing the initial condition:

The equation becomes:

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The particular solution to the given differential equation ( \frac{dy}{dx} = -\frac{x}{y} ) with the initial condition ( y(1) = -\sqrt{2} ) is ( y(x) = -\sqrt{x^2 + 1} ).

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