Results 1 to 2 of 2

Thread: Differential Equation help...

  1. #1
    Super Member
    Joined
    Feb 2008
    Posts
    535

    Differential Equation help...

    Hello, I'm a newbie when it comes to differential equations and my professor assigned some problems that we never went over in class. Hopefully someone can help...

    y' = 2y; y(x) = Ce^(2x), y(0) = 3.

    Here are the directions: First verify that y(x) satisfies the given differential equation. Then determine a value of the constant C so that y(x) satisfies the given initial condition.

    I have to do about 10 of these, so if anyone could go through the steps on how to solve this, I will greatly appreciate it. Thanks for your time...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    12,880
    Thanks
    1946
    $\displaystyle \frac{dy}{dx} = 2y$

    $\displaystyle \frac{1}{y}\,\frac{dy}{dx} = 2$

    $\displaystyle \int{\frac{1}{y}\,\frac{dy}{dx}\,dx} = \int{2\,dx}$

    $\displaystyle \int{\frac{1}{y}\,dy} = 2x + C_1$

    $\displaystyle \ln{|y|} + C_2 = 2x + C_1$

    $\displaystyle \ln{|y|} = 2x + C_1 - C_2$

    $\displaystyle |y| = e^{2x + C_1 - C_2}$

    $\displaystyle |y| = e^{C_1 - C_2}e^{2x}$

    $\displaystyle y = \pm e^{C_1 - C_2}e^{2x}$

    $\displaystyle y = Ce^{2x}$ where $\displaystyle C = \pm e^{C_1 - C_2}$.


    Now use the inital condition $\displaystyle y(0) = 3$

    $\displaystyle 3 = Ce^{2\cdot 0}$

    $\displaystyle 3 = C$.


    Therefore $\displaystyle y = 3e^{2x}$.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Partial Differential Equation satisfy corresponding equation
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: May 16th 2011, 07:15 PM
  2. Replies: 4
    Last Post: May 8th 2011, 12:27 PM
  3. Replies: 1
    Last Post: Apr 11th 2011, 01:17 AM
  4. Partial differential equation-wave equation - dimensional analysis
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: Aug 28th 2009, 11:39 AM
  5. Replies: 13
    Last Post: May 19th 2008, 08:56 AM

Search Tags


/mathhelpforum @mathhelpforum