Formulario equacoes.

Prévia do material em texto

UNA
Formula´rio - Equac¸o˜es Diferenciais
dy
dx
=
g(x)
h(y)
⇒
∫
h(y)dy =
∫
g(x)dx
y′ =
dy
dt
= ky y(t) = y0e
kt y(0) = y0
dP
dt
= kP
(
1− P
K
)
P (t) =
K
1 + Ae−kt
A =
K − P0
P0
y(0) = y0
dT
dt
= k(T − Ts) T (t) = Ts + (T0 − Ts)ekt
y′ + P (x)y = Q(x) I(x) = e
∫
P (x)dx
1