Book: Mathematics Part-II
Chapter: 9. Differential Equations
Subject: Maths - Class 12th
Q. No. 7 of Exercise 9.3
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Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.
We know that the equation of the parabola having the vertex at origin and the axis along the positive y- axis is
x2 = 4ay ------(1)
Now, differentiating equation (1) w.r.t. x, we get,
2x = 4ay’ -----(2)
On dividing equation (2) by equation (1), we get,
⇒ xy’ = 2y
⇒ xy’ – 2y = 0
Therefore, the required differential equation is xy’ – 2y = 0.
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