MYTUTOR SUBJECT ANSWERS

507 views

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 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.

 

 

Stephen S. GCSE Maths tutor, A Level Maths tutor

2 years ago

Answered by Stephen, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

296 SUBJECT SPECIALISTS

£20 /hr

Leo P.

Degree: Theoretical Physics (Masters) - University College London University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“About Me: I am a MSci Theoritical Physics student at University College London (UCL). Maths is everywhere and that's what I love about maths. Hopefully you'll enjoy it too I am a friendly, understanding and patient tutor that enjoys t...”

£20 /hr

Ben M.

Degree: Mathematics and Physics (Masters) - Bath University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
.STEP.

“I am a second year student at the university of Bath, studying an integrated masters in Maths and Physics. Currently have 3 years experience in tutoring.”

MyTutor guarantee

£30 /hr

Will H.

Degree: Engineering Design (Masters) - Bristol University

Subjects offered:Maths

Maths

“My sessions are based around worked examples as it's without a doubt the best way to learn how to tackle mathematical concepts! ”

MyTutor guarantee

About the author

Stephen S. GCSE Maths tutor, A Level Maths tutor

Stephen S.

Currently unavailable: for new students

Degree: Earth Sciences (Masters) - Durham University

Subjects offered:Maths

Maths

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

You may also like...

Other A Level Maths questions

Find the general solution, in degrees, of the equation 2sin(3x+45°)=1. Use your general solution to find the solution of 2sin(3x+45°)=1 that is closest to 200 °.

Prove that between every two rational numbers a/b and c/d, there is a rational number (where a,b,c,d are integers)

How do I find dy/dx for the following equation: (x^2) + 2y = 4(y^3) + lnx?

How can we remember the difference between differentiation and integration?

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok