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Calculate the power $e^3$
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$\frac{dx}{dy}+y=e^{3}x$
Learn how to solve differential equations problems step by step online. Solve the differential equation dx/dy+y=e^3x. Calculate the power e^3. We need to isolate the dependent variable x, we can do that by simultaneously subtracting y from both sides of the equation. Rearrange the differential equation. We can identify that the differential equation has the form: \frac{dy}{dx} + P(x)\cdot y(x) = Q(x), so we can classify it as a linear first order differential equation, where P(y)=-e^{3} and Q(y)=-y. In order to solve the differential equation, the first step is to find the integrating factor \mu(x).