Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

This discussion is now closed.

Check out other Related discussions

MEI C4 Differential Equations

Obtain a particular solution to (1-e^2y)dy/dx = e^y

Given that y=1 when x=2.
There is no need to express y in terms of x.

Any ideas?

\frac{1-e^{2y}}{e^y}dy=dx

e^{-y}-e^ydy=dx

\int e^{-y}-e^y\ dy=\int 1\ dx

-e^{-y}-e^y=x+C

Pheylan

\frac{1-e^{2y}}{e^y}dy=dx

e^{-y}-e^ydy=dx

\int e^{-y}-e^y\ dy=\int 1\ dx

-e^{-y}-e^y=x+C

carry on.. :wink:

:wink:

ziedj

carry on.. :wink:

:wink:

-e^{-1}-e^1=2+C

C=-(e+\frac{1}{e}+2)

-e^{-y}-e^y=x-(e+\frac{1}{e}+2)

e+\frac{1}{e}+2=x+e^y+\frac{1}{e^y}

Pheylan

-e^{-1}-e^1=2+C

C=-(e+\frac{1}{e}+2)

-e^{-y}-e^y=x-(e+\frac{1}{e}+2)

e+\frac{1}{e}+2=x+e^y+\frac{1}{e^y}

You have passed the test. One internet will be sent your way.

Solved the solution up to substituting the x and y values and was about to post when i scrolled down and saw Pheylan's answer :sigh:

:sigh:

OP

Pheylan

\frac{1-e^{2y}}{e^y}dy=dx

e^{-y}-e^ydy=dx

\int e^{-y}-e^y\ dy=\int 1\ dx

-e^{-y}-e^y=x+C

so is x + e^-y + e^y = 4 the particular solution?

Hippysnake

so is x + e^-y + e^y = 4 the particular solution?

this is:

Pheylan

-e^{-1}-e^1=2+C

C=-(e+\frac{1}{e}+2)

-e^{-y}-e^y=x-(e+\frac{1}{e}+2)

e+\frac{1}{e}+2=x+e^y+\frac{1}{e^y}

Hippysnake

so is x + e^-y + e^y = 4 the particular solution?

where did 4 come from? :s-smilie:

:s-smilie:

time.to.dance

Solved the solution up to substituting the x and y values and was about to post when i scrolled down and saw Pheylan's answer :sigh:

:sigh:

sorry

:awesome:

OP

Cheers dude. How about this one?

x^2 dy/dx - y^2 =0?

I end up with y = x + c but that seems a bit too easy...

\frac{dy}{dx}=\frac{y^2}{x^2}

y^{-2}dy=x^{-2}dx

\int y^{-2}\ dy=\int x^{-2}\ dx

-y^{-1}=-x^{-1}+C

-\frac{1}{y}=-\frac{1}{x}+C

-x=-y+Cxy

y=x+Cxy

OP

Pheylan

\frac{dy}{dx}=\frac{y^2}{x^2}

y^{-2}dy=x^{-2}dx

\int y^{-2}\ dy=\int x^{-2}\ dx

-y^{-1}=-x^{-1}+C

-\frac{1}{y}=-\frac{1}{x}+C

-x=-y+Cxy

y=x+Cxy

I got x/1+cx?

Ah well, I have one more question?

At time t seconds the rate of increase in the concentration of flesh eating bugs in a controlled environment is proportional to the concentration C of bugs present. Initially C= 100 bugs and after 2 seconds there are five times as many.

Write down a differential equation connection dC/dt, C and t and hence find an expression for C in terms of t.

Related discussions

Latest

Trending

Trending

Articles for you

Students react after A-level Maths Paper 1 on 6 June 2023

Students react after A-level Maths Paper 1 on 6 June 2023

Students react after A-level Maths Paper 2 on 13 June 2023

Students react after A-level Maths Paper 2 on 13 June 2023

What is an LLM and how could it benefit your career?

What is an LLM and how could it benefit your career?

Powerful questions business students forget to ask their career advisers

Powerful questions business students forget to ask their career advisers