Separability Differential equations (a), (b), and (c) are separa- ble. Equation (d) is not separable: it resists all efforts to segregate its variables. (What goes wrong when you try to separate part (d)?) dy (a) dt + ydy = -t dt y dy = 1'y dy = 1²dt y (b) ip dy (c) = y +1 dt dy = dt y +1 dy (d) =t + y (not separable) ip

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Separability Differential equations (a), (b), and (c) are separa-
ble. Equation (d) is not separable: it resists all efforts to segregate its variables.
(What goes wrong when you try to separate part (d)?)
dy
(a)
dt
+ ydy = -t dt
y
dy
= 1'y
dy = 1²dt
y
(b)
ip
dy
(c)
= y +1
dt
dy = dt
y +1
dy
(d)
=t + y (not separable)
ip
Transcribed Image Text:Separability Differential equations (a), (b), and (c) are separa- ble. Equation (d) is not separable: it resists all efforts to segregate its variables. (What goes wrong when you try to separate part (d)?) dy (a) dt + ydy = -t dt y dy = 1'y dy = 1²dt y (b) ip dy (c) = y +1 dt dy = dt y +1 dy (d) =t + y (not separable) ip
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