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

What is a solution to the differential equation $\frac{dy}{dx}=2x$?
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wegpluktee3
Writing
$dy=2xdx$
and integrating we get
$y={x}^{2}+C$
This equation is separable.

listgrein6u
More details
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
$f\prime \left(x\right)=g\left(x\right)$, then this means $f\left(x\right)=\int g\left(x\right)dx$
Our f'(x) is essentially dy and our g(x)=2x. We now have
$y=\int 2xdx$
Integrating with the reverse power rule, we get
$y={x}^{2}+C$