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

Question

Briley Riley

Mathematics

27 May, 07:23

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

+4

Answers (1)

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Melody Buck · 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

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

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