Question

From the differential equation by eliminating the arbitrary constant from y square=4ax

Answer 1

SOLUTION

TO DETERMINE

From the differential equation by eliminating the arbitrary constant from y² = 4ax

EVALUATION

Here the given equation is

y² = 4ax - - - - - (1)

Here a is constant

Differentiating both sides of Equation 1 with respect to x we get

$\sf{2yy_1 = 4a}$

Putting the value of 4a in Equation 1 we get

$\sf{ {y}^{2} = 2yxy_1}$

$\sf{ \implies \: y = 2xy_1}$

$\sf{ \implies \: 2xy_1 = y}$

FINAL ANSWER

Hence the required differential equation is

$\sf{ 2xy_1 = y}$

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