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Verizon [17]
3 years ago
5

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

Advanced Placement (AP)
1 answer:
AysviL [449]3 years ago
3 0

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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