Results 1 to 2 of 2

Thread: Ln Equations Formation

  1. #1
    Super Member
    Joined
    Sep 2007
    Posts
    528
    Awards
    1

    Ln Equations Formation

    I need help with these four questions (If possible, can it be explained in steps):

    1.
    $\displaystyle \sin x \frac{\mathrm{d}y}{\mathrm{d}x} = e^y,$ $\displaystyle 0<x<\pi,$ $\displaystyle y=0 at x=\frac{\pi}{2}$

    2.
    $\displaystyle \sin x \frac{\mathrm{d}y}{\mathrm{d}x} = \tan y (3\cos x + \sin x),$ $\displaystyle y=\frac{\pi}{6} at x=\frac{\pi}{2}$

    3.
    $\displaystyle (5-3\sin x) \frac{\mathrm{d}y}{\mathrm{d}x} = 40\cos x,$ $\displaystyle y=0 at x=\frac{3\pi}{2}$

    4.
    $\displaystyle \frac{1}{y} \frac{\mathrm{d}y}{\mathrm{d}x} = x + xy,$ $\displaystyle y=1 at x=0$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    1) $\displaystyle \displaystyle\frac{dy}{e^y}=\frac{dx}{\sin x}$
    $\displaystyle \displaystyle\int\frac{dy}{e^y}=\int\frac{dx}{\sin x}$

    2) $\displaystyle \displaystyle\frac{dy}{\tan y}=\frac{3\cos x+\sin x}{\sin x}dx$
    $\displaystyle \displaystyle\int\cot ydy=\int(1+3\cot x)dx$

    3) $\displaystyle \displaystyle\frac{dy}{y(y+1)}=xdx$
    $\displaystyle \displaystyle\int\frac{dy}{y(y+1)}=\int xdx$

    Now, integrate.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Need help with formation of basis in R3
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: Feb 23rd 2011, 04:30 PM
  2. Crater formation math
    Posted in the Geometry Forum
    Replies: 2
    Last Post: Apr 29th 2010, 03:36 PM
  3. Replies: 3
    Last Post: Feb 27th 2009, 07:05 PM
  4. standard enthalpies of formation
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: Oct 13th 2008, 02:55 PM
  5. Replies: 1
    Last Post: Jul 29th 2007, 02:37 PM

Search Tags


/mathhelpforum @mathhelpforum