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

asked Oct 28, 2021 167k views

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1 vote

Answer:

$y=2√(\sin \left(x\right)-1),\:y=-2√(\sin \left(x\right)-1)$

Step-by-step explanation:

$(dy)/(dx)=(\cos \left(x\right))/(y)2$

$y'\:=(\cos \left(x\right))/(y)\cdot \:2$

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

$yy'\:=2\cos \left(x\right):\quad (y^2)/(2)=2\sin \left(x\right)+c_1$

$(y^2)/(2)=2\sin \left(x\right)-2$

$y=2√(\sin \left(x\right)-1),\:y=-2√(\sin \left(x\right)-1)$

John Bartels answered Nov 1, 2021

6.2k points

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