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
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.