Q. 19

Mark the correct alternative in each of the following:

The equation of the curve satisfying the differential equation

y(x + y3)dx = x(y3 – x) dy and passing through the point (1, 1) is

A. y3 – 2x + 3x2y = 0

B. y3 + 2x + 3x2y = 0

C. y3 + 2x – 3x2y = 0

D. none of these

Answer :

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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