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Question
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
x3 + y3 = 4ax
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Solution
x3 + y3 = 4ax .....(1)
Differentiating both sides w.r.t. x, we get
`3"x"^2 + 3"y"^2 "dy"/"dx" = 4"a" xx 1`
∴ `3"x"^2 + 3"y"^2 "dy"/"dx" = 4"a"`
Substituting the value of 4a in (1), we get
`"x"^3 + "y"^3 = (3"x"^2 + 3"y"^2 "dy"/"dx")"x"`
∴ `"x"^3 + "y"^3 = 3"x"^3 + 3"xy"^2 "dy"/"dx"`
∴ `2"x"^3 + 3"xy"^2 "dy"/"dx" - "y"^3 = 0`
This is the required D.E.
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