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Find the general solution of the given differential equations. Give the largest interval I over which the general solution is defined. Determine whether there are any transient terms in the general solution.


y' + 2xy = (x^3)


ydx = (y(e^y) - 2x)dy


(dP)/(dt) + 2tP = P + 4t - 2

Verified Answer :

nobillionaireNobley

The general solution of y' + 2xy = (x^3) is y(x) = c1e^(-x^2)

The general solution of ydx = (y(e^y) - 2x)dy is x = c1/(y(x))^2 + (e^y(x) ((y(x))^2 - 2y(x) + 2)/(y(x))^2
The general solution of (dP)/(dt) + 2tP = P + 4t - 2 is P(t) = c1e^(t - t^2) + 2

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