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Question

Find the equation of a curve passing through the point (−2, 3), given that the slope of the tangent to the curve at any point (x, y) is 2xy2.

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Solution

We have,dydx=2xy2y2dy=2x dxIntegrating both sides, we gety2dy=2x dxy33=x2+C .....1Now the given curve passes theough -2, 3Therefore, when x=-2, y=3 Substituting x=-2 and y=3 in 1 we get333=-22+C 9=4+CC=5Putting the value of C in 1, we gety33=x2+5y3=3x2+15y=3x2+1513

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