find the general solution of the given differential equation. (x + 1) dy dx + (x + 2)y = 2xe−x

Find the general solution of the given differential equation.

(x + 1) dy/dx + (x + 2)y = 2xe^?x

^y=

Give the largest interval I over which the general solution is defined. (Think about the implications of any singular points.)

(??, ?)

(0, 1)

(?1, ?)

(0, ?)

(??, 1)

Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.)

Solve the given initial-value problem. Give the largest interval I over which the solution is defined.

xy’ + y = e^x, y(1) = 8

Solve the given initial-value problem. Give the largest interval I over which the solution is defined.

Ldi/dt + Ri = E, i(0) = i₀, L, R, E, i₀ constants

i =

I =