Question

form differential equation for curve y square =4ax​

Answer 1

Answer:

Should I solve for X or Y?

Step-by-step explanation:

Answer 2

Answer: Hence differential equation for curve y² = 4ax is $\frac{dy}{dx} = \frac{\sqrt{a} }{\sqrt{x} }$

Step-by-step explanation:

Here given  curve is   y²  =  4ax  ..........................(1)

Taking square root on both sides, We get

$\sqrt{y^{2} } = \sqrt{4ax} \\ y = 2\sqrt{ax} \\ y = 2\sqrt{a} \sqrt{x}$

Differentiate on both side w.r.t. x of equation (1)

$\frac{d(y^{2}) }{dx} =\frac{d(4ax)}{dx} \\2y\frac{dy}{dx} = 4a\\divide by 2y on both sides, we get\\\frac{dy}{dx} = \frac{2a}{y} \\\frac{dy}{dx} = \frac{2a}{2\sqrt{ax} } \\\frac{dy}{dx} = \frac{a}{\sqrt{a} \sqrt{x} }\\\frac{dy}{dx} = \frac{\sqrt{a} }{\sqrt{x} }$

Hence differential equation for curve y² = 4ax is $\frac{dy}{dx} = \frac{\sqrt{a} }{\sqrt{x} }$