Question

Find an equation of the curve that passes thro. the pt (0,1) and whose slope at (x,y) is xy

I would like a FAIR hint please, not the answer.

Answer 1

Differential equations for sure

Answer 2

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Answer 3

Is this a tricky version of y = mx + b?

Answer 4

Because I could do:

y = (xy)*x + b

Answer 5

the gradient or \(\frac{dy}{dx}\) is 'xy'
you need to find the equation by integrating both sides

Answer 6

I understand that "xy" will be on one side, but what will be on the other?

Answer 7

Ok so the (0,1) portion is telling me that this is an INITIAL VALUE PROBLEM.

Answer 8

\[\frac{dy}{dx}=xy\]
\[\frac{1}{y}\frac{dy}{dx}=x\]
\[\large \int\limits \frac{1}{y}\frac{dy}{dx} \, dx\text{ = }\int\limits x \, dx\]
Do the math and then sub (0,1) to find the constant

Answer 9

So this is some function s.t. when we take the derivative of at some point (x,y) we get xy

Answer 10

yes, so when you integrate, you'll get back the equation or function

Answer 11

Got it. Thanks.

Answer 12

welcome