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  • Which of the following differential equations has y = x as one of its particular solution? (A) (B) (C) (D)

12.    Which of the following differential equations has y = x as one of its particular solution?

            (A)    \frac{d^2y}{dx^2} - x^2\frac{dy}{dx} + xy =x

            (B)    \frac{d^2y}{dx^2} + x\frac{dy}{dx} + xy =x

            (C)    \frac{d^2y}{dx^2} - x^2\frac{dy}{dx} + xy =0

            (D)    \frac{d^2y}{dx^2} + x\frac{dy}{dx} + xy =0

Answers (1)

best_answer

Given equation is 
y = x
Now, on differentiating it w.r.t x
we get,
\frac{dy}{dx} = 1
and again  on differentiating it w.r.t x
we get,

\frac{d^2y}{dx^2} = 0
Now, on substituting the values of \frac{d^2y}{dx^2} , \frac{dy}{dx} \ and \ y  in all the options we will find that only option c which is  \frac{d^2y}{dx^2} - x^2\frac{dy}{dx} + xy =0  satisfies 
Therefore, the correct answer is (C)

Posted by

Gautam harsolia

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