D.E. of family of parabolas symmetrical about the X-axis is

y \frac{d^{2} y}{d x^{2}} + {(\frac{d y}{d x})}^{2} = 0

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y \frac{d^{2} y}{d x^{2}} - {(\frac{d y}{d x})}^{2} = 0

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- y \frac{d^{2} y}{d x^{2}} + {(\frac{d y}{d x})}^{2} = 1

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y^{2} \frac{d^{2} y}{d x^{2}} + {(\frac{d y}{d x})}^{2} = 1

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Solution

The correct option is A $y \frac{d^{2} y}{d x^{2}} + {(\frac{d y}{d x})}^{2} = 0$
Equation of family of parabolas symmetrical about x-axis:
$y^{2} = 4 a (x - h)$
Differentiating both sides, we get
$2 y \frac{d y}{d x} = 4 a$
Differentiating both sides, we get
$2 y \frac{d^{2} y}{d x^{2}} + 2 {(\frac{d y}{d x})}^{2} = 0$
$y \frac{d^{2} y}{d x^{2}} + {(\frac{d y}{d x})}^{2} = 0$ .

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Similar questions

Q. Degree of

y \frac{d^{2} y}{d x^{2}} = {[3 + {(\frac{d y}{d x})}^{2}]}^{\frac{2}{3}}

is:

The differential equation of family of curves $y^{2} = 4 a (x + a)$ is
a) $y^{2} = 4 \frac{d y}{d x} (x + \frac{d y}{d x})$
b) $2 y \frac{d y}{d x} = 4 a$
c) $y \frac{d^{2} y}{d x^{2}} + {(\frac{d y}{d x})}^{2} = 0$
d) $2 x \frac{d y}{d x} + y {(\frac{d y}{d x})}^{2} - y = 0$

Q. The number of arbitrary constants in the general solution of

y \frac{d^{2} y}{d x^{2}} + (\frac{d y}{d x})^{2} = sin x

is ___

Q. The number of arbitrary constants in the general solution of

y \frac{d^{2} y}{d x^{2}} + (\frac{d y}{d x})^{2} = s i n x

= ___

Q. If

x = cos θ, y = {sin}^{3} θ

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D.E. of family of parabolas symmetrical about the X-axis is

The correct option is A yd2ydx2+(dydx)2=0Equation of family of parabolas symmetrical about x-axis:y2=4a(x−h)Differentiating both sides, we get2ydydx=4aDifferentiating both sides, we get2yd2ydx2+2(dydx)2=0yd2ydx2+(dydx)2=0.