# 代写Math – Math Problem

### 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) = .
``````
##### 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
``````dy
``````y (0) =  y 0 .)