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How do you find the general solution to #y'=sqrtx/e^y#?

Answer 1

Aurora Alvarado

I found: #y=ln[2/3x^(3/2)+c]#

Have a look:

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Answer 2

William Abdalla

To find the general solution to the differential equation (y' = \sqrt{x}/e^y), follow these steps:

Separate variables by moving all (y)-related terms to one side and all (x)-related terms to the other side.
Integrate both sides with respect to (x).
Solve for (y) to obtain the general solution.
Include an arbitrary constant to represent all possible solutions.

The general solution to the given differential equation is:

[y = -2\ln(\sqrt{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.