Question

For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation. (i) (ii) (iii) (iv)

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Solution

(i) Differentiating both sides with respect to x, we get: Again, differentiating both sides with respect to x, we get: Now, on substituting the values of and in the differential equation, we get: â‡’ L.H.S. â‰  R.H.S. Hence, the given function is not a solution of the corresponding differential equation. (ii) Differentiating both sides with respect to x, we get: Again, differentiating both sides with respect to x, we get: Now, on substituting the values of and in the L.H.S. of the given differential equation, we get: Hence, the given function is a solution of the corresponding differential equation. (iii) Differentiating both sides with respect to x, we get: Again, differentiating both sides with respect to x, we get: Substituting the value of in the L.H.S. of the given differential equation, we get: Hence, the given function is a solution of the corresponding differential equation. (iv) Differentiating both sides with respect to x, we get: Substituting the value of in the L.H.S. of the given differential equation, we get: Hence, the given function is a solution of the corresponding differential equation.

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