Find general solution of following separable differential equation a) (dy/dx) = (xe^(y^2-1)) / (y(x-5))

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The differential equation is $\"\"$ .

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Find the general solution using variable seperable method.

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$\"\"$

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Integrate on both sides.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Apply logarithm on each side.

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$\"\"$

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$\"\"$ , where $\"\"$ .

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Find general solution of following linear differential equation a) x^2(dy/dx) + 3xy = 12x^8

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(2a)

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The differential equation is $\"\"$ .

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Rewrite the differential equation.

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$\"\"$

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$\"\"$

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The equation is in the form of linear differential equation $\"\"$ .

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Solution of first order linear differential equation $\"image\"$ is

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$\"image\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Solution of the differential equation is $\"\"$ .

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(3b)

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The differential equation is $\"\"$ .

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The equation is in the form of linear differential equation $\"\"$ .

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Solution of first order linear differential equation $\"image\"$ is $\"image\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Step 2:

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Consider $\"\"$ .

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Apply integration by parts: $\"image\"$ .

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Let $\"\"$ .

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Apply derivative on each side.

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$\"\"$

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Let $\"\"$ .

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Apply integral on each side.

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ in equation (1).

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$\"\"$

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$\"\"$

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$\"\"$

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Solution of the differential equation is $\"\"$