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  • The Integrating Factor of the differential equation x dy/dx - y = 2 x ^ 2 is (A) e^-x (B) e^-y (C) 1/x (D) x

Q18.    The Integrating Factor of the differential equation x\frac{dy}{dx} - y = 2x^2 is

            (A)    e^{-x}

            (B)    e^{-y}

            (C)    \frac{1}{x}

            (D)    x

Answers (1)

best_answer

Given equation is
x\frac{dy}{dx} - y = 2x^2
we can rewrite it as
\frac{dy}{dx}-\frac{y}{x}= 2x
Now, 
It is    \frac{dy}{dx}+py=Q  type of equation  where p = \frac{-1}{x} \ and \ Q = 2x
Now,
I.F. = e^{\int pdx} = e^{\int \frac{-1}{x}dx}= e^{\int -\log x }= x^{-1}= \frac{1}{x}
Therefore, the correct answer is (C)

Posted by

Gautam harsolia

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