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Nonamiya [84]
2 years ago
12

If you answer this, thank you! Please show all the work.

Advanced Placement (AP)
1 answer:
sp2606 [1]2 years ago
4 0

Answer:

a

Explanation:

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Find the solution to the differential equation dy/dx = cos(x) / y2 , where y(π/2) = 0.
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Answer:

y=2\sqrt{\sin \left(x\right)-1},\:y=-2\sqrt{\sin \left(x\right)-1}

Explanation:

\frac{dy}{dx}=\frac{\cos \left(x\right)}{y}2

y'\:=\frac{\cos \left(x\right)}{y}\cdot \:2

yy'\:=2\cos \left(x\right)

yy'\:=2\cos \left(x\right):\quad \frac{y^2}{2}=2\sin \left(x\right)+c_1

\frac{y^2}{2}=2\sin \left(x\right)-2

y=2\sqrt{\sin \left(x\right)-1},\:y=-2\sqrt{\sin \left(x\right)-1}

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