Banner Ad 1

Collapse

Announcement

Collapse
No announcement yet.

Oofah! Differential Equations problem

Collapse
This topic is closed.
X
X
 
  • Filter
  • Time
  • Show
Clear All
new posts

  • Oofah! Differential Equations problem

    I'm desparately trying to solve this - yes, it's for a homework assignment, I'd much rather someone give me a hint, instead of solving it for me -

    y''=-6exp(y)

    I'm trying to solve it by setting dy/dx = v, and dv/dx=(dv/dy)*(dy/dx)=v*dv/dx, so v*v'=-6exp(y) (which is an already separated first order ODE).

    (v^2)/2=-6exp(y)+c1 ; since v is dy/dx, you can set the right side equal to v(multiply by 2 and take the square root), divide by the right to separate again, and integrate with respect to y

    v^2=-12exp(y)+c1 (2*c=a different constant, but still constant).
    v=+- (c1-12exp(y))^(1/2)
    dy/dx=+- (c1-12exp(y))^(1/2)
    int(((c1-12(exp(y)))^-(1/2))dy)=int(dx)

    solve the left with a trigonometric substitution, 12exp(y)=c*cos^2(t)

    I won't show all of my work at this juncture, but I'm running into problems after the integration, and just want some advice (am I doing this right? On the right track? Hopelessly lost?).

  • #2
    I absolutely should state that this is an IVP, with y(0)=0 and y'(0)=6

    Comment


    • #3
      y= ln(112+64*(3^.5))-2 ln((7+4*(3^.5))*exp(-4*(3^.5)*x)+1)-4*(3^.5)*x
      or
      y= ln(112-64*(3^.5))-2 ln((7-4*(3^.5))*exp(-4*(3^.5)*x)+1)-4*(3^.5)*x

      Comment

      Working...
      X