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Find the particular solution of the dif...

Find the particular solution of the differential equation `(dy)/(dx)=-4x y^2`given that `y = 1`, when`x = 0`.

Text Solution

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The correct Answer is:
`(dy)/(dx)=-4xy^2`
`(dy)/y^2=-4xdx`
integrating both side
`-y^(-1)=-4x^(2)/2+c`
`y^(-1)-2x^2+C=0(1)`
given y=1 and x=0
1-0+C=0
C=-1
putting this value in equation (1)
`y^(-1)-2x^2-1=0`
`(dy)/(dx)=-4xy^2`
`(dy)/y^2=-4xdx`
integrating both side
`-y^(-1)=-4x^(2)/2+c`
`y^(-1)-2x^2+C=0(1)`
given y=1 and x=0
1-0+C=0
C=-1
...
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