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Rewrite the differential equation using Leibniz notation
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$x^8\frac{dy}{dx}+9x^7y=e^{-171x}$
Learn how to solve problems step by step online. Solve the differential equation x^8y^'+9x^7y=e^(-171x). Rewrite the differential equation using Leibniz notation. Divide all the terms of the differential equation by x^8. Simplifying. 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(x)=\frac{9}{x} and Q(x)=\frac{e^{-171x}}{x^8}. In order to solve the differential equation, the first step is to find the integrating factor \mu(x).