Question

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

Answer 1

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