代写Math – 这是一个数学相关的题目
Math Problem
Current Score :
1. /1 pointsSEssCalcET2 7.7.003.
Solve the differential equation. (Use C for any needed constant. Your response should be in the form 'y=f(x)'.)
2. /1 pointsSEssCalcET2 7.7.008.
Solve the differential equation. (Use C for any needed constant. Your response should be in the form 'z=f(t)'.)
3. /1 pointsSEssCalcET2 7.7.009.
Find the solution of the differential equation that satisfies the given initial condition.
4. /1 pointsSEssCalcET2 7.7.012.
Find the solution of the differential equation that satisfies the given initial condition.
Differential Equations (Homework)
Katie Wu
math 212, section 001, Spring
Instructor: Thang Nguyen
WebAssign
Last Saved : n/a Saving... ()
xy^2 y' = x + 5
+ 7 et + z =
dz
dt
dy = ,
dx
x
y
y (0) = 3
dP = 2 ,
dt
Pt P (1) = 5
5. /1 pointsSEssCalcET2 7.7.013.
Find the solution of the differential equation that satisfies the given initial condition.
where a is a constant.
6. /1 pointsSEssCalcET2 7.7.015.
Find an equation of the curve that passes through the point (0, 1) and whose slope at ( x , y ) is
7. /1 pointsSEssCalcET2 7.7.016.
Find the function f ( x ) such that and (Use f for in your equation.)
y’ tan( x ) = a + y , y ( /3) = a , 0 < x < /2,
9 xy.
f ' ( x ) = f ( x )(1 f ( x )) f (0) = .
1
15
f ( x )
8. /2 pointsSEssCalcET2 7.7.022.
Match the differential equation with its direction field.
Give reasons for your answer.
on the lines and
The slopes at each point are independent of y , so the slopes are the same along each line parallel to the y axis. Note that
for
on the line and on the line
on the lines and and for
The slopes at each point are independent of x , so the slopes are the same along each line parallel to the x axis. Note that
for
y' = x ( 10 y )
y' = x (10 y ) = 0 x = 0 y = 10.
y = 10, y' = 0.
y' = x (10 y ) = 0 y = x + 1/10, y' = 1 y = x.
y’ = x (10 y ) = 0 x = 0 y = 0, y’ > 0 0 < x < /10,0 < y < /10.
y = 10, y' = 0.
9. /3 pointsSEssCalcET2 7.7.039.
One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population
who have heard the rumor and the fraction who have not heard the rumor.
(a) Write a differential equation that is satisfied by y . (Use k for the constant of proportionality.)
(b) Solve the differential equation. (Let
(c) A small town has 4000 inhabitants. At 8 AM, 320 people have heard a rumor. By noon half the town has heard it. At
what time will 90% of the population have heard the rumor? (Do not round k in your calculation. Round your final
answer to one decimal place.)
hours after 8 AM
=
dy
dt
y (0) = y 0 .)