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Notice that integration is simply the opposite of differentiation. So, if we just integrate this term-by-term then we can find an expression of y in terms of x.

So, when we integrate dy/dx becomes ...

Remember that the equation of a straight line (when given two points OR a point and a gradient) is y-y_1 = m(x-x_1) where m is the gradient and (x_1,y_1) is a point on the line.

Since we have two p...

Rates and differential equations is a topic many students find difficult, especially when solving the differential equation is combined with techniques from other topics on the C4 syllabus. I hope my walk...

Firstly we must notice that we can differentiate each term separately.

Starting with the 2xy term, we must use the product rule as x and y are two variable that will differentiate. Setting u=2x and...

To see where the graph is greater than zero, we start by finding where it meets zero. By factorising (x^2 - 7x - 18), we find it equals (x-9)(x+2). The expression equals zero at the points x = 9 and x = -...