Final answer to the problem
$y=\left(e^x\cdot x-e^x+C_0\right)x^{4}$
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Step-by-step Solution
Learn how to solve integration by parts problems step by step online. Solve the differential equation xy^'-4y=x^6e^x. Rewrite the differential equation using Leibniz notation. Divide all the terms of the differential equation by x. 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{-4}{x} and Q(x)=x^{5}e^x. In order to solve the differential equation, the first step is to find the integrating factor \mu(x).
Final answer to the problem
$y=\left(e^x\cdot x-e^x+C_0\right)x^{4}$
