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Solve dy/dx+ycotx=2x+x^2cotx,given that ...

Solve `dy/dx+ycotx=2x+x^2cotx`,given that y=0 when x=0

Text Solution

Verified by Experts

Comparing the given equation with first order differential equation,
`dy/dx+Py = Q(x)`, we get, `P = cotx and Q(x) = 2x+x^2cotx`
So, Integrating factor `(I.F) = e^(intcotxdx)`
`I.F.= e^(ln|sinx|) = sinx`
we know, solution of differential equation,
`y(I.F.) = intQ(I.F.)dx`
`:.`Our solution will be,
...
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