What is a solution to the differential equation \frac{dy}{dx}=2x?

Ramiro Grant

Ramiro Grant

Answered question

2022-04-19

What is a solution to the differential equation dydx=2x?

Answer & Explanation

Sabrina Campos

Sabrina Campos

Beginner2022-04-20Added 13 answers

Explanation:
Writing
dy=2xdx
and integrating we get
y=x2+C
This equation is separable.
Juan Goodwin

Juan Goodwin

Beginner2022-04-21Added 10 answers

Let's get a dx on the right so we can integrate. This can be done by multiplying both sides by dx. We now have
dy=2xdx
If we have
f'(x)=g(x), then this means f(x)=g(x)dx
Our f'(x) is essentially dy and our g(x)=2x. We now have
y=2xdx
Integrating with the reverse power rule, we get
y=x2+C

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