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What is the general solution of the differential equation? : # dy/dx = 1/x^2 #

Answer 1

Emily Ammerman

# y =-1/x + C #

We have:

# dy/dx = 1/x^2 #

We can "separate the variables" in this First Order Separable Ordinary Differential Equation to obtain:

# int \ dy = int \ 1/x^2 \ dx #

Since both integrals are typical calculus outcomes, integrating yields:

# y = x^(-1)/(-1) + C # # \ \ = -1/x + C #

Which is the Whole Solution?

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Answer 2

Isabella Ackerman

The general solution of the given differential equation ( \frac{dy}{dx} = \frac{1}{x^2} ) is ( y = -\frac{1}{x} + C ), where ( C ) is the constant of integration.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.