Solve the following differential equation by finding an appropriate integrating factor

Question

 Solve the following differential equation by finding an appropriate integrating factor

-xdx+(3y-x^2y)dy=0

Constant =??

I have calculated 1/2y^2+1/2ln|3-x^2|= c & y^2+ln|3-x^2|

both however are incorrect can someone please help me?

Answer 1

I AGREE!!!!

-x dx + (3y-x^2 y) dy = 0

-x dx + y( 3-x^2) dy = 0

y(3-x^2) dy = x dx

y dy = x dx /(3-x^2)

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integral x * dx / (3-x^2)

U = 3 - x^2

dU = -2x dx

(-1/2) dU = x dx

integral: (-1/2) dU / U

= (-1/2) ln U

= (-1/2) ln |3 - x^2|

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Integrates both sides then:

(1/2)y^2 = (-1/2) ln | 3- x^2| + c

y^2 = c - ln |3-x^2|

y = sqrt( c - ln |3-x^2|)