Unit 8

Calculus Level 1

Find the general solution to the differential equation d y d x = x . \frac{dy}{dx}=x.

y = e x + c y = e^x + c y = e x y = e^x y = A e x y = Ae^x y = 1 2 x 2 + c y = \frac{1}{2} x^2+c y = 1 2 x 2 y = \frac{1}{2} x^2

Andrew Potter by Andrew Potter , 37, United Kingdom

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1 solution

Andrew Potter
Jun 21, 2015

The right-hand side is a function of the independent variable only, so we can use direct integration.

y = ∫ x d x y = 1 2 x 2 + c . y = \int x dx \\ y = \frac{1}{2} x^2 + c.

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