Home > Calculus > Solving Separable Differential Equations

What is a solution to the differential equation #dy/dx=ky#?

Answer 1

Luke Alvarez

# abs y = C e^(kx)#

Assiuming k is just some constant, this is immediately separable

#1/y y' = k#

And #int (1/y y' = k) dx#

#implies int 1/y \ dy = k int dx#

#implies ln abs y = k x + C#

# abs y = e^(k x + C) = C e^(kx)#

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Answer 2

Paisley Johnson

The solution to the differential equation ( \frac{dy}{dx} = ky ) is given by ( y(x) = Ce^{kx} ), where ( C ) is a 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.

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