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Hi!Please help me with this problem:I must to demonstrate this function y=x^3/2 + C/x^3...

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jojo92g | Student, Undergraduate | (Level 1) eNoter

Posted October 23, 2012 at 3:05 PM via web

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Hi!Please help me with this problem:I must to demonstrate this function y=x^3/2 + C/x^3 is a solution for this differential equation: dy/dx+3y/x=3x^2

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tiburtius | High School Teacher | (Level 3) Associate Educator

Posted October 28, 2012 at 7:08 PM (Answer #1)

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Simply insert your `y` in differential equation:

`(dy)/(dy)+3y/x=(3x^2)/(2)-(3C)/(x^4)+((3x^2)/(2)+(3C)/(x^3))/(x)=`

`(3x^6-6C+3x^6+6C)/(2x^4)=(6x^6)/(2x^4)=3x^2`

which is what you were supposed to get.

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