# AP Calculus Help Five Questions

1. Find the particular solution to y " = 2sin(x) given the general solution y = -2sin(x) + Ax + B and the initial conditions y(pi/2) = 0 and y'(pi/2) = -2.

2. What function is a solution to the differential equation y ' - y = 0?

3. If dy/dx = cos^2(pi*y/4) and y = 1 when x = 0, find the value of x when y = 3.

4. The differential equation dy/dx = (x+1)/(x-2):
I.produces a slope field with horizontal tangents at x = -1
II.produces a slope field with vertical tangents at x = 2
III.produces a slope field with rows of parallel segments
Select those that are true.

5. If dy/dx = x*y^2 and if y = 1 when x = 0, then what is x when y = 3?

1. 👍 1
2. 👎 0
3. 👁 1,413
1. #1 is just like your other post, only you have to use two steps.
y" = 2sin(x)
y' = -2cosx+A
-2 = -2cos(π/2) = 0+A so A=-2
y' = -2cosx-2
y = -2sinx-2x+B
0 = -2sin(π/2)-2(π/2)+B = -2-π+B so B=2+π
y = -2sinx-2x+π+2

#2 This you can do by inspection: you know that d/dx(e^x) = e^x
Or, you can go through the trouble of finding the integrating factor.

#3
dy/dx = cos^2(pi*y/4)
dy = cos^2(π/4 y) dx
dy/cos^2(π/4 y) = dx
sec^2(π/4 y) dy = dx
(4/π)tan(π/4 y) = x+c
since y(0)=1,
(4/π)tan(π/4) = 0+c
4/π = c
(4/π)tan(π/4 y) = x + 4/π
when y=3, we have
(4/π)tan(π/4*3) = x+4/π
(4/π)(-1) = x+4/π
x = -8/π

#4
is (x+1)/(x-2)=0 at x = -1?
is it undefined when x=2?
does the slope change with changes in y?

#5 is just like #3
dy/dx = x*y^2
dy/y^2 = x dx
-1/y = 1/2 x^2+c
y = -1/(1/2 x^2+c) = -2/(x^2+c) (different c but who cares?)
now just plug in (0,1) to find c

1. 👍 1
2. 👎 0

## Similar Questions

Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. NOTE: when I write + it has a minus on the bottom too x^2+7=0 a. x= +7 b. x = +3.5 c. x= 0 d. no solution ***

asked by a on April 4, 2017
2. ### Math

1. What is the solution of n^-49=0 A. -7 B. 7 C. += 7*** Sorry I couldn't find this symbol D. no solution 2. What is the solution of x^2+64=0? A. -5 B. 8 C. += 8 D. no solution*** 3.What is the side length of a square with an area

asked by Charlotte Dunois on March 7, 2019
3. ### Chemistry

You have 3.00 L of a 2.37 M solution of NaCl(aq) called solution A. You also have 2.00 L of a 2.00 M solution of AgNO3(aq) called solution B. You mix these solutions together, making solution C. Calculate the concentration (in M)

asked by tina on May 6, 2011
4. ### Chemistry

What is the activity coefficient of H^+ in a solution containing 0.073 M HCl and 0.0090 M Ca(ClO4)2? What is the pH of the solution? I believe I have to find the ionic strength of the solution first, but I don't know how to find

asked by Sam on February 4, 2013
5. ### calculus

Find the particular solution to y ′ = sin(x) given the general solution is y = C − cos(x) and the initial condition y(pi/2)=1

asked by Anonymous on July 17, 2015
1. ### AP Calculus

Find the particular solution to y ' = 2sin(x) given the general solution is y = C - 2cos(x) and the initial condition y(pi/2) = 1

asked by Tom on March 26, 2018
2. ### chemistry

Which of the answer choices correctly describes a solution that has less of a solute dissolved in it than the maximum amount possible for a given temperature and pressure? colloidal solution saturated solution supersaturated

asked by malia on September 21, 2017
3. ### science

1. Which of the following is TRUE regarding this situation: Solution A has a pH of 7.38, and Solution B has a pH of 7.42? a.Solution B is more acidic than Solution A b.The pH of Solution A falls within the homeostatic pH range for

asked by a on January 28, 2013
4. ### Calculus

Find the particular solution to y"=3sin(x) given the general solution y=-3sin(x) +Ax+B and the initial conditions y (π/2)=π and y'(π/2)=2

asked by Alice on March 3, 2019
5. ### CHEM.

1. a) What species are present in a 3.0 M NH3 solution? b) Qualitatively, what is the pH of this solution? c) What reaction(s) might occur when this solution is added to a solution containing Mn2+? d) What effect will adding HNO3

asked by Anonymous. on April 6, 2014