Stephen S.

Currently unavailable: for new students

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.

If you would like to meet me please click the 'Free meet the tutor request' button at the top right of the page.

#### Subjects offered

SubjectLevelMy prices
Maths A Level £20 /hr
Maths GCSE £18 /hr

#### Qualifications

MathematicsA-LevelA
BiologyA-LevelA
PhysicsA-LevelB
 CRB/DBS Standard No CRB/DBS Enhanced No

### How do i solve differential equations?

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 side...

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.

For example:

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.

∫ (y+1) 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 = x+ 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.

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2 years ago

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