Question

Answer this question, hurry up guys❓​

Answer 1

Differential Equation is  x (dy/dx) - y = 2x^2

Dividing both sides by 'x',

=> (dy/dx) - (y/x) = (2x^2)/x

=> (dy/dx) - (y/x) = 2x

Differential Equation is of the form

(dy/dx) + P₁x = Q₁

Where P₁ = -1/x and Q₁ = 2x

Thus,

$IF = e^{\int pdx}$

$=> e^{-\frac{1}{x} dx}$

$=> IF = e^{-logx}$

$=> IF = e^{logx^{-1} }$

$=> IF = x^{-1}$

$=> IF = \frac{1}{x}$

Therefore, the answer is Option(C)

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