Results 1 to 2 of 2

Math Help - Differential Equations

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    7

    Differential Equations

    Can anyone help me solve the following differential equation that satisfies the given initial condition?

    dP/dt=4(sqrt of Pt)

    where P(1) =7

    When I did it, I got P=(1/12p^3/2 + sqrt of 7 - 1/2)^2.

    Can anyone figure out what i'm doing wrong?? Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by Jessica098 View Post
    Can anyone help me solve the following differential equation that satisfies the given initial condition?

    dP/dt=4(sqrt of Pt)

    where P(1) =7

    When I did it, I got P=(1/12p^3/2 + sqrt of 7 - 1/2)^2.

    Can anyone figure out what i'm doing wrong?? Thanks.
    I think what you have is this

    \frac{dP}{dt}=4\sqrt{Pt}=4\sqrt{P}\sqrt{t}

    Now seperating variables we get

    \frac{dP}{\sqrt{P}}=4\sqrt{t}dt

    remaining equality we see that

    \int\frac{dP}{\sqrt{P}}=\int{4\sqrt{t}}dt\Rightarr  ow{2\sqrt{P}=\frac{8}{3}t^{\frac{3}{2}}+C}

    Solving for P we get

    P=\bigg(\frac{4}{3}t^{\frac{3}{2}}+C\bigg)^2

    Can you go from there?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. 'Differential' in differential equations
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: October 5th 2010, 10:20 AM
  2. Replies: 2
    Last Post: May 18th 2009, 03:49 AM
  3. Differential Equations
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 12th 2009, 05:44 PM
  4. Replies: 5
    Last Post: July 16th 2007, 04:55 AM
  5. Replies: 3
    Last Post: July 9th 2007, 05:30 PM

Search Tags


/mathhelpforum @mathhelpforum