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Find the particular solution of the differential equation  x^3 dy/dx = 2 given y = 3 ,...

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mastertja | Student | eNotes Newbie

Posted April 26, 2012 at 7:11 PM via web

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

given y = 3 , X= 1

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Matthew Fonda | eNotes Employee

Posted April 26, 2012 at 7:20 PM (Answer #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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