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Anonymous
timer Asked: Jan 18th, 2021

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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

Unformatted Attachment Preview

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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