Verify y = log x + c is the solution of differential equation xd2ydx2+dydx = 0 - Mathematics and Statistics

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Sum

Verify y = log x + c is the solution of differential equation `x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0

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Solution

y = log x + c

Differentiating w.r.t. x, we get

`("d"y)/("d"x) = 1/x`

∴ `x ("d"y)/("d"x)` = 1

Again, differentiating w.r.t. x, we get

`x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0

∴ Given function is a solution of the given differential equation.

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Chapter 1.8: Differential Equation and Applications - Q.4

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