Thread: Differential Equation Curve

A curve rises from the origin continuously in the

xy plane into the first quadrant. The area under the curve from (0, 0) to (x, y) is 1/3 the area of the rectangle with these points as opposite vertices. Find the differential equation satisfied by the curve.

Thanks for your help!

Originally Posted by JoAdams5000

A curve rises from the origin continuously in the

xy plane into the first quadrant. The area under the curve from (0, 0) to (x, y) is 1/3 the area of the rectangle with these points as opposite vertices. Find the differential equation satisfied by the curve.

Thanks for your help!

Let be the curve so the area under the curve is



and the rectangle is so the equation to your question is



and differentiating gives