Solve the following initial value problem for u as a function of t:


du/dt + (k/m) u = 0 (k and m positive constants), u(0) = u₀


b. as a separable equation.

28. Derivation of Equation (7) in Example 4

a. Show that the solution of the equation

di /dt + R/Li = V/L

is

i = V/R + Cexp(-(R/L)i) .

In Exercises 1–22, solve the differential equation.

2y' - y = xe^(x/2)

Solve the following initial value problem for u as a function of t:

du/dt + (k/m) u = 0 (k and m positive constants), u(0) = u₀

a. as a first-order linear equation.