What is a solution to the differential equation $\frac{d y}{d x} = \frac{6 sin x}{y}$ $dy/dx=(6sinx)/y$ ?

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Answer 1 · 2016-07-25T13:51:40

$y = \pm \sqrt{C - 12 cos x}$ $y = pm sqrt( C -12 cosx)$

$\frac{d y}{d x} = \frac{6 sin x}{y}$ $dy/dx=(6sinx)/y$

separable!

$y \frac{d y}{d x} = 6 sin x$ $y dy/dx=6sinx$

$int \ y dy/dx \ dx=int \ 6sinx \ dx$

$int \ d/dx(1/2 y^2) \ dx=int \ 6sinx \ dx$

$1/2 y^2 = -6 cosx + C$

$y = pm sqrt( C -12 cosx)$

What is a solution to the differential equation dy/dx=(6sinx)/ydydx=6sinxydy/dx=(6sinx)/y?