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First find the general solution to the differential equation y'' + 4y' + 3y = 0 as an arbitrary number of the solution to this differential equation can be added to the solution of the differential equati...

First draw a diagram to see the set-up.Then look at SUVAT to see which values we have been given. In this case it is a=4, u=3,v=18 and s=?. The only letter not used from SUVAT is the t so we use the formu...

The most important thing to note about this question is that we must differentiate implicitly. We must differentiate each term with respect to x. Using our differentiation rules we can see that our first ...

The stationary points of the function are the points at which the gradient is equal to 0. (If you draw out a standard y=x^3 graph, you can see the gradient is 0 at the points where the graph changes direc...

There are a few ways of solving these simultaneous equations, but most of them involve substitution. Perhaps the most intuitive substitution to make is the second equation (y=3x+5) into the first one (xy=...