Differentiate dy⁄dt=t^2-y

Answer 1

This is a standard first order differential equation with constant coefficients in the form

dy/dt + y = f(t)

There is a closed form solution derived from using the integration factor e^t times every term

e^ty' + e^ty = d(e^ty)/dt = t²e^t

Integrate and rearrange: y(t) = e^-t(integral of t²e^tdt) = e^-t((t²-2t +2)e^t + C) = Ce^-t + t² -2t + 2

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