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

driliwra7 2022-09-15 Answered
What is a solution to the differential equation d y d x = 2 x ?
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Answers (2)

wegpluktee3
Answered 2022-09-16 Author has 12 answers
Writing
d y = 2 x d x
and integrating we get
y = x 2 + C
This equation is separable.

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listgrein6u
Answered 2022-09-17 Author has 1 answers
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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
d y = 2 x d x
If we have
f ( x ) = g ( x ) , then this means f ( x ) = g ( x ) d x
Our f'(x) is essentially dy and our g(x)=2x. We now have
y = 2 x d x
Integrating with the reverse power rule, we get
y = x 2 + C

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