How do you integrate dy/dx=(1+2x)*sqrt(y)?



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Posted on (Answer #1)

We'll solve this separable differential equation in this way:

- first, we'll divide both sides by `sqrt(y)`

dy/dx*`sqrt(y)` = 1 + 2x

- now, we'll multiply both sides by dx:

dy/`sqrt(y)` = (1+2x)dx

- we'll integrate both sides:

`int` dy/`sqrt(y)` = `int` (1+2x)dx

2`sqrt(y)` = `int` dx + `int` 2x dx

2`sqrt(y)` = x + 2x^2/2 + C

`sqrt(y)` = x/2 + x^2/2 + C/2

We'll raise to square both sides to remove the square root from the left side:

y = (x + x^2 + C)^2/4

The requested primitive function is y = (x + x^2 + C)^2/4.

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