The solution of the differential equation $$x3dydx+4x2tany=ex$$ secy satisfying $$y1=0$$ is

Correct option is 2siny=ex(x-1)x-4

Questions

$The solution of the differential equation x^{3} \frac{dy}{dx} + 4 x^{2} tany = e^{x} secy satisfying y (1) =0 is$

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tany=(x-2)exlogx

siny=ex(x-1)x-4

tany=(x-1)exx-3

siny=ex(x-1)x-3

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detailed solution

Correct option is B

x4cosydy+4x3sin⁡y=xex→∫dx4siny=∫xexdx⇒x4sin⁡y=ex(x−1)+c−⋯−−−1Pass⁡(1,0)⇒c=0→x4sin⁡y=ex(x−1)→sin⁡y=ex(x−1)x4

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The solution of the differential equation x3dydx+4x2tany=ex secy satisfying y1=0 is

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$The solution of the differential equation x^{3} \frac{dy}{dx} + 4 x^{2} tany = e^{x} secy satisfying y (1) =0 is$