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Question
Verify y = log x + c is the solution of differential equation `x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0
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) xx 1` = 0
∴ `x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0
∴ y = log x + c is the solution of `x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0
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