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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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The differential equation `dy/dx= 8x^2y^2` has to be solved.
=> `(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`
Posted by justaguide on May 8, 2013 at 3:25 AM (Answer #2)
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