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First we must ensure that the differential is i the standard form of y' + p(x) y = f(x)The we use the integration factor I(x) = e to the integral of p(x)we then realise that if we differentiate this we wi...

Firstly when proving something by induction, we always show that the base case works, i.e. we plug in n=1. In this case we get 4² + 5¹ =21, which is divisible by 2...

This question gives hints as to how you should solve it. Because it tells you the angle between the line and the plane, this should indicate that doing something to do with finding the angle between the l...

Firstly, we know that dy/dx is the gradient of the tangent to a curve. If we know the gradient of the tangent, and the point on the curve where the tangent touches it, we can work out the equation of the ...

The first step in tackling any second order differential equation is to find the Auxiliary Function. Looking at the equation's left hand side, we can find the derivative terms - we will s...