math 250 Online exam
math代做 – 这个题目属于一个express的代写任务, 涵盖了express/math等方面
Midterm Exam Winter 2023
A math 250 Online exam
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- Find the general solutions (implicit or explicit) to the following equations.
[4] (a) y(x)y(x) =x y^5
(b)
dy
dx
=
2 x^3 x y^2
x^2 y 2 y^3
[4]
[4] (c) y 2 y+y=exsin(x)
- Consider the DEy(x) = (y1)^2 (y2),
[4] (a) Sketch the direction field and determine the intervals of increase/decrease and intervals of concavity. Then sketch the solution curves for the initial conditions (ICs)y(0) = 0. 5 , 0. 5 , 1. 5 , 1. 9 , 2. 5.
[3] (b) Based on the direction field (a), determine how the behaviour of the so- lutionsyfor largex(i.e., asx+) depends on different initial values ofyatx= 0.
- (a) Consider the following IVP,[3]
y(x) =
10
3
x y^2 /^5 , y(0) = 1
Using the existence and uniqueness theorem, what can you predict about
the solution.
(b) Solve the IVP from part (a).[3]
- Consider the following IVP:[4]
d^2 x
dt^2
=
g R^2
(x+R)^2
, x(0) = 0 ,
dx
dt
(0) =v 0
Heregis the gravitational acceleration (m/s^2 ),Ris the radius of the earth (m),
andv 0 is the initial velocity (m/s). Choose appropriate variables and write this
IVP in a non-dimensional form.
- Solve the following equations.
[4] (a) x yy(ln(x y)1) = 0
[3] (b) y= 1 + (y)^2