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1.Determine the order of the given differential equation and its linearity.

(a).(1+y2)d2ydt2+tdydt+y=et

(b).dydt+ty2=0

(c).d3ydt3+tdydt+¿

2.Draw a direction filed for the given differential equation, and discuss its behavior of y as t→∞.

(a).y'=2y−3

the given function is a solution of the differential equation.

y' '+2 y'−3 y=0; y1 (t )=e−3 t , y2(t )=et

4. Solve the IVP problems and plot the solutions (using calculator) for serval values of y0. Then

describe in a few words how the solutions resemble, and differ from, each other.

dy

dt

=−y+5 , y (0)=y0

Worksheet #1
Name: _______________
Class Section: _________________ Date: _______________
1. Determine the order of the given differential equation and its linearity.
2
( 1+ y 2 ) d y2 + t dy + y =et
(a).
dt
dt
(b).
dy
2
+t y =0
dt
(c).
d 3 y dy
+t + ¿
dt
d t3
2. Draw a direction filed for the given differential equation, and discuss its behavior of y as t → ∞ .
'
(a).
y =2 y−3
(b).
y ' =− y (5− y )
3. Verify the given function is a solution of the differential equation.
''
'
−3 t
t
y +2 y −3 y=0; y 1 ( t )=e , y 2 ( t )=e
4. Solve the IVP problems and plot the solutions (using calculator) for serval values of y 0. Then
describe in a few words how the solutions resemble, and differ from, each other.
dy
=− y +5 , y ( 0 )= y 0
dt
...

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