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solve the differential equation dy/dx= 8x^2y^2 with the condition that y(2)=3 the...

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rmunoz90 | Student, Undergraduate | (Level 1) Salutatorian

Posted May 8, 2013 at 2:05 AM via web

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solve the differential equation dy/dx= 8x^2y^2 with the condition that y(2)=3

the solution to the equation is y=

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 8, 2013 at 3:25 AM (Answer #2)

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The differential equation `dy/dx= 8x^2y^2` has to be solved.

`dy/dx= 8x^2y^2`

=> `(1/y^2)*dy = 8*x^2*dx`

take the integral of both the sides

`int (1/y^2)*dy = 8*int x^2*dx`

=> `-1/y = 8*x^3/3`

=> `y = -3/(8x^3) + C`

It is given that y(2) = 3

`3 = -3/64 + C`

=> `C = 3 + 3/64 = 195/64`

The function `y = -3/(8x^3) + 195/64`

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oldnick | (Level 1) Valedictorian

Posted May 8, 2013 at 2:22 AM (Answer #1)

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`dy/dx=8x^2y^2`    

 

`(dy)/y^2= 8x^2 dx`

 

`-1/y=8/3 x^3`

`y=-3/(8x^3)+c`

Since:  `y(2)=3 rArr`  `3=-3/64 +c` 

`c=189/64` 

 

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