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Solve the differential equation e^(x) ta...

Solve the differential equation `e^(x) tan y dx + (1-e^(x))sec^(2) y dy = 0`

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To solve the differential equation \( e^{x} \tan y \, dx + (1 - e^{x}) \sec^{2} y \, dy = 0 \), we will rearrange and separate the variables. ### Step 1: Rearranging the equation We can rewrite the equation as: \[ e^{x} \tan y \, dx = - (1 - e^{x}) \sec^{2} y \, dy \] Dividing both sides by \( (1 - e^{x}) \tan y \sec^{2} y \): ...
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