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Degree: Earth Sciences (Masters) - Durham University
Maths has always been a subject that is very clear to me. It's a subject which I enjoy and am enthusiastic about and this is what drives me to teach others maths. Having spent the first year of my sixth form tutoring a GCSE class every week I have good experience in teaching students. I was tutoring students of ranging abilities to achieve and surpass their target grades.
The exact nature of the tutorial itself is down to the students however in all my tutorials I will aim to teach the student the correct notation (something that is often overlooked), how to approach maths problems and good exam technique.
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|Maths||A Level||£20 /hr|
To solve differential equations we use a method called separation of variables. This is where we take all the ‘y’ values to one side of the equation and all the ‘x’ values to the other side of the equation make sure the ‘y’ terms are on the same side as the ‘dy/dx’. We then integrate both sides of the equation with respect to the variable of that side. We then if possible rearrange to equation with respect to y.
Solve this differential equation.
dy/dx = (3x2)/(y+1)
Step 1: Rearrange the equation so that the ‘y’ terms are on one side of the equation and the ‘x’ terms are on the other side of the equation.
Times both sides by: (y+1).
(y+1)dy/dx = 3x2
Step 2: Integrate both sides with respect to x.
dx dy/ dx = ∫ 3x2 dx
(The ‘dx’s cancel on the left side of the equation leaving ‘dy’, this means we integrate the left side with respect to ‘y’ now).
∫ (y+1) dy = ∫ 3x2 dx
(y2/2) + y = x3 + c
(You only need one constant in the solution for differential equations.)
It is not possible to rearrange this equation with respect to y so we leave it as it is.