Form the differential equation from the following primitives wher… - Vidyadip

Question

Form the differential equation from the following primitives where constants are arbitrart:

$\text{y}^2=4\text{ax}$

✓

Answer

The equation of family of curves is

$\text{y}^2=4\text{ax}$

where a is an arbitrary constant. This equation contains only one arbitrary constant, so we shall get a differential equation of first order.

Differentiating equation (1) with respect to x, we get

$2\text{y}\frac{\text{dy}}{\text{dx}}=4\text{a}$

$\Rightarrow\frac{\text{y}}{2}\frac{\text{dy}}{\text{dx}}=\text{a}\ ...(2)$

Putting the value of a in equation (1), we get

$\text{y}^2=4\frac{\text{y}}{2}\frac{\text{dy}}{\text{dx}}\text{x}$

$\Rightarrow\text{y}=2\text{x}\frac{\text{dy}}{\text{dx}}$

It is the required differential equation.

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