solve second-order initial value problem

y"(x)= x e^-2x
y'(0)= 0
y(0)= 0

  1. 👍 0
  2. 👎 0
  3. 👁 74
asked by Mina
  1. First you need to integrate y"(x). This looks like a situation where "integration by parts" can be used.
    Let u(v) = x and dv = e^-2x dx
    du = dx v = (-1/2)*e^-2x
    Integral of u dv = uv - integral of v du
    = (-x/2)e(-2x) + Integral of(1/2)*e^-2x dx
    Finish that off and use the y'(0) = 0 condition to solve for the arbitary constant. Once you have dy/dx, integrate again and use the initial condition at y(0) for the y(x) solution.

    1. 👍 0
    2. 👎 0
    posted by drwls

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Solve the first-order initial value problem using half angle formulas {y'(x)= 1 + sin^2 x y (0)= -7

    asked by Mina on May 14, 2008
  2. Child development

    Using these steps, consider a cognitive “problem” a young child might encounter that he/she needs help with (such as putting together a puzzle, sequencing – putting items in order, sorting by color or size, adding,

    asked by amy on October 14, 2011
  3. Chemistry

    I know how to find half-lives, but I have trouble finding the length of time it would take for the concrentration of X to decrease to Y% of its initial value. For example, this is one of the problems: Methyl isocyanide, CH3NC,

    asked by Rachel on December 16, 2006
  4. Circuits and electronics applications3

    We are presented with a familiar first-order circuit: a capacitor driven by a Thevenin source. Now we have a sinusoidal drive that starts at t=0. so the differential equation is RCdv(t)dt+v(t)=vI(t)=Vicos⁡(ωt)u(t) and we are

    asked by sengeni on November 25, 2016
  5. Algebra

    A worker drops a hammer from a second story roof that is 10m above the ground. Choose the appropriate formula to use where t represents time in seconds after the hammer is dropped. h(t) = -16t2 +v0 (Initial Velocity) + h0 (Initial

    asked by Meena on February 21, 2016
  6. Physics

    When you see a traffic light turn red, you apply the brakes until you come to a stop. Suppose your initial speed was 12.9 m/s, and you come to rest in 35.0 m. How much time does this take? Assume constant deceleration. What

    asked by Chad on October 4, 2012
  7. algebra 1b

    Solve the problem by stating the equation you would use to solve and then solving it. After receiving discount of 12.5% on its bulk order of printer paper, johns office supply pays $3200 . what was the price of the order before

    asked by Dee on June 11, 2012
  8. Chemistry

    This problem is 1st order for half life. How long would it take for the concentration of cyclopropane to decrease to 50% of its initial value? to 25% of its initial value? Rate constant is 9.2/s I set up like this... t1/2=

    asked by Chris on January 21, 2013
  9. Math

    How do you solve second order initial value problems? I don't understand how would solve these questions..for example (d^2 y)/(dx^2 )=24x^2-10. When x=1, dy/dx = 3, and y = 5. Can anyone explain how?

    asked by Fabian on April 24, 2008
  10. Physics

    You can use any coordinate system you like in order to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity v at an angle θ with respect

    asked by Malorie on February 5, 2014

More Similar Questions