Recent content by Kaylee!

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...

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?

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...

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?

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...