contestada

Which of the following is the solution to the differentiable equation dy/dx=4x/y, where Y(2)=-2
a.)y=2x for x>0
b.)y=2x-6 for x does not equal 3
c.)y=--sqrt(4x^2)-12 for x>sqrt3
d.)y=sqrt(4x^2)-12 for x>sqrt3

Respuesta :

chikafujiwara

First we'll substitute [tex]\frac{dy}{dx}[/tex] with [tex]y'[/tex]

[tex]y'=\frac{4x}{y}[/tex]

Then we can separate this.

[tex]yy'=4x[/tex]

Then we'll solve this.

[tex]yy'=4x: \frac{y^2}{2}=2x^2+c_1[/tex]

[tex]\frac{y^2}{2}=2x^2-6[/tex]

[tex]y=2\sqrt{x^2-3},y=-2\sqrt{x^2-3}[/tex]

Then we'll plug in to find the extraneous solutions (if any)

[tex]y=-2\sqrt{x^2-3}[/tex]

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