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

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Answer 1 · 2018-07-15T12:09:53

#y=x^2+C#

Writing

#dy=2xdx#
and integrating we get

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

Answer 2 · 2018-07-15T17:00:51

#y=x^2+C#

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!