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Question
Solve
`dy/dx + 2/ x y = x^2`
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Solution
`dy/dx + 2/ x y = x^2`
The given equation is of the form
`dy/dx + py = Q`
`where, P = 2/x and Q = x^2`
∴ I.F. =`e^(int^(pdx) = e^(2int^(1/xdx) e = ^(2logx) = e^(logx^2) = x^2`
∴ Solution of the given equation is
`y(I.F.) = int Q(I.F.) dx + c_1`
`y(x^2) = int x^2 xx x^2 dx + c_1`
∴ `x ^2 y = x^4 intdx + c_1`
∴ `x^2 y = x^5/5 + c_1`
∴ 5x2 y = x5 + c …[c = 5c1]
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