What is a solution to the differential equation dy/dx=2x?

2 Answers
Jul 15, 2018

y=x^2+C

Explanation:

Writing

dy=2xdx
and integrating we get

y=x^2+C
This equation is separable.

Jul 15, 2018

y=x^2+C

Explanation:

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)=int g(x) dx

Our f'(x) is essentially dy and our g(x)=2x. We now have

y=int2xdx

Integrating with the reverse power rule, we get

y=x^2+C

Hope this helps!