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** Step-by-step Solution **

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Rewrite the differential equation using Leibniz notation

Learn how to solve differential equations problems step by step online.

$\frac{dy}{dx}=x+8$

Learn how to solve differential equations problems step by step online. Solve the differential equation y^'=x+8. Rewrite the differential equation using Leibniz notation. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Expand the integral \int\left(x+8\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.

** Final answer to the problem

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