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

Respond to this Question

First Name

Your Response

Similar Questions

  1. ALGEBRA CHECK ANSWERS

    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

You can view more similar questions or ask a new question.