Find the solution of the differential equation `dy/dx=(ln x)/(xy)` that satisfies the given initial condition y(1)=2

Expert Answers

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It is given that `dy/dx = (ln x)/(x*y)` and `y(1) = 2`

`dy/dx = (ln x)/(x*y)`

=> `y*dy = (ln x/x) dx`

Integrate both the sides

=> `y^2/2 = (ln x)^2/2 + C`

=> `y^2 = (ln x)^2 + C`

As `y(1) = 2`

=> `2^2 = 0 + C`

=> `C = 4`

`y^2 = (ln x)^2 + 4`

The solution of the differential equation is `y^2 = (ln x)^2 + 4`

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