Q. 19

# Mark the correct alternative in each of the following:The equation of the curve satisfying the differential equationy(x + y3)dx = x(y3 – x) dy and passing through the point (1, 1) isA. y3 – 2x + 3x2y = 0B. y3 + 2x + 3x2y = 0C. y3 + 2x – 3x2y = 0D. none of these

y(x + y3)dx = x(y3 – x)dy

yx dx + y4 dx = xy3 dy – x2 dy

xy3 dy – x2 dy – yx dx – y4 dx = 0

y3 [x dy – y dx] – x[x dy + y dx] = 0

Divide both sides by y2x3 we get,    Integrating both sides we get,   -- (1)

Now the given curve is passing through the point (1, 1)  Substituting value of C in (1) we get,  y3 + 2x = 3x2y

y3 + 2x – 3x2y = 0 = (C) is the required solution.

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