separatio of variables

posted by .

solve the initial value problem by separation of variables dy/dx=6x^2y and y(0)=4

  • separatio of variables -

    ydy=6x^2 dx

    y^2/2=2x^3 + C

    y(0)=4
    16/2=C

  • separatio of variables -

    dy/y = 6 x^2 dx
    ln y = 2 x^3 + c

    when x = 0, y = 4
    ln 4 = c
    so
    ln y = 2 x^3 + ln 4

    ln (y/4) = 2 x^3

    or
    y/4 = e^(2x^3)
    y = 4 e^(2x^3)

  • separatio of variables -

    damon is correct, I lost y.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    solve the initial value problem by separation of variables dy/dx=y^(2)+1, y(1)=0
  2. calculus

    solve the initial value problem by separation of variables 8. dy/dx=x+1/xy, x>0, y(1)=-4
  3. separation of variables

    solve the initial value problem by separation of variables dy/dx=x2/y given y=-5 when x=3
  4. calculus

    solve the initial value problem by separation of variables dy/dx=-x^2y^2, y(4)=4
  5. calculus

    solve the initial value problem by separation of variables dy/dx=-xy^2, y(1)=-0.25
  6. separation of variables

    solving the initial value problem by separation of variables dy/dx=(4(sqrt of y)lnx))/x, y(e)=9
  7. calculus

    solve the initial value problem by separation of variables dy/dx=-xy^2, y(1)=-0.25
  8. calculus

    solve the initial value problem by separation of variables dy/dx=-x^2y^2, y(4)=4
  9. separation of variables

    solve the value problem by separation of variables dy/dx=x^2/y when y=-5 and x=3
  10. calculus

    how do you solve the initial value problem by separation of variables dy/dx=-x^2y^2, y(4)=4

More Similar Questions