Find the particular solution of the differential equation x^3 dy/dx = 2

given y = 3 , X= 1

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We must solve the differential equation:

`x^3 dy/dx = 2`

The first step is to notice that this is a separable equation, so we will separate:

`dy = 2/x^3 dx`

Next, we can integrate both sides:

`int dy = int 2/x^3 dx`

`\implies y = -1/x^2 + c`

We have now found the general solution, and can proceed to solve the initial value problem. We'll plug in y=3 and x=1:

`3 = -1/1 + c \implies c=4`

**Therefore our final solution is** `y = -1/x^2 + 4`

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