Recent content by Kaylee!

  1. K

    Why does separation of variables work?

    To solve a separable ODE like this I would simply multiply each side by dx and then integrate both sides. However, I know that it is only notational convenience that allows me to do this, and what's really going on is slightly more complicated. Take this DE for example...
  2. K

    DiffEQ: Determining the largest interval of a solution

    I'm multiplying both sides of the equation by secx, which has a domain of (-pi/2, pi/2), so that's the interval. Is this reasoning correct?
  3. K

    DiffEQ: Determining the largest interval of a solution

    The question is to determine the solution to the following 1st order linear DE, along with the largest interval the solution is valid on: cosx \frac{dy}{dx} + (sinx)y=1 Rewriting it shows it to be linear: \frac{dy}{dx} + (tanx)y = secx The intergrating factor is: e^{\int{tanx...
  4. K

    Simplifying a rational expression

    I've done a calculus problem. The LHS is my answer and the RHS is the answer in the book. \frac{2(x-1)^2}{(x^2-1)^2} = \frac{2}{(x+1)^2} What was done to simplify this equation?
  5. K

    Solving an inverse trig equation

    Homework Statement Solve for x arcsin(2x) + arccos(x) = \frac{\pi}{6} Homework Equations The Attempt at a Solution Subtracting arccos(x) from both sides and then taking the sine of both sides: 2x = sin\left[\frac{\pi}{6} - arccos(x)\right] Applying the difference angle...
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