Solve the differential equation:

To solve the given differential equation 

\[\frac{dy}{dx}\frac{-\tan y}{1+x}=(1+x)e^x\sec y,\]

we can rewrite it to separate variables and integrate both sides. Here's how:

\[\frac{dy}{dx}\frac{-\tan y}{1+x}=(1+x)e^x\sec y\]

Multiplying both sides by \((1+x)\sec y\) to clear the fraction, we get:

\[\frac{dy}{dx}(-\tan y) = (1+x)e^x\]

Now, we separate variables:

\[\frac{dy}{-\tan y} = (1+x)e^x dx\]

Integrate both sides:

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