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The differential equation corresponding to the family of curves y=c(x-c)2, where c is a constant, is :
  • a)
    4y²=8xyy'-(y')²
  • b)
    8y²=4xyy'-(y')³
  • c)
    8y²=4xy'+(y')³
  • d)
    y²=xyy'-(y)²
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The differential equation corresponding to the family of curves y=c(x-...
The differential equation corresponding to the family of curves y=c(x-c)2 can be found by differentiating the equation with respect to x.

First, expand the equation:

y = c(x^2 - 2cx + c^2)
y = cx^2 - 2c^2x + c^3

Now, differentiate both sides with respect to x:

dy/dx = 2cx - 2c^2

So, the differential equation corresponding to the family of curves is:

dy/dx = 2cx - 2c^2
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The differential equation corresponding to the family of curves y=c(x-c)2, where c is a constant, is :a)4y²=8xyy-(y)²b)8y²=4xyy-(y)³c)8y²=4xy+(y)³d)y²=xyy-(y)²Correct answer is option 'B'. Can you explain this answer?
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