# Q.3.find the integrating factor and solve the exact solution consider the differential equation (e^(x-y)cosy+cosx+2e^(2x-y)dx + (sinx-e^(x-y)siny+3y^2e^-y)dy Q.5. Prove ?

See below.

so we have the differential equation

Now

Now

Integrating we have

and finally

hence

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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