The Student Room Group

Further Maths Differential Equation

questoin1.JPG
Attachment not found

So I tried with the working shown but the equation is not proven when I sub them back to the equation. Could anyone please help?
i did it like this:

dv/dx = 3y2dy/dx

d2v/dx2 = 3y2d2y/dx2 + 6y(dy/dx)2

= 3( 25e-2x - 3y3 + 6y2dy/dx )

= 75e-2x - 9y3 + 18y2dy/dx

= 75e-2x -9v + 6dv/dx

etc
Reply 2
Original post by the bear
i did it like this:

dv/dx = 3y2dy/dx

d2v/dx2 = 3y2d2y/dx2 + 6y(dy/dx)2

= 3( 25e-2x - 3y3 + 6y2dy/dx )

= 75e-2x - 9y3 + 18y2dy/dx

= 75e-2x -9v + 6dv/dx

etc


Yeah I think that's an easier way of approach, I'm just confused why these two methods give different answers, though.
Original post by sourmango1
Yeah I think that's an easier way of approach, I'm just confused why these two methods give different answers, though.


I haven't tried it, but it should give the same answer as far as I can see.

Post your working if you're not getting it.
Reply 4
Original post by RDKGames
I haven't tried it, but it should give the same answer as far as I can see.

Post your working if you're not getting it.


workingfull.JPG
So this is my full working. The problem seems to be the term in (dy/dx)^2 since it doesn't cancel out, but the rest of the terms are correct.
Original post by sourmango1

So this is my full working. The problem seems to be the term in (dy/dx)^2 since it doesn't cancel out, but the rest of the terms are correct.


Error shown below.

It should be 2y(dydx)2=2y(13y2dvdx)2=29y3(dvdx)2\displaystyle 2y \left( \dfrac{dy}{dx} \right)^2 = 2y \left( \dfrac{1}{3y^2} \dfrac{dv}{dx} \right)^2 = \dfrac{2}{9y^3} \left( \dfrac{dv}{dx} \right)^2

which then cancels with the other.

(edited 5 years ago)
Reply 6
Original post by RDKGames
Error shown below.

It should be 2y(dydx)2=2y(13y2dvdx)2=29y3(dvdx)2\displaystyle 2y \left( \dfrac{dy}{dx} \right)^2 = 2y \left( \dfrac{1}{3y^2} \dfrac{dv}{dx} \right)^2 = \dfrac{2}{9y^3} \left( \dfrac{dv}{dx} \right)^2

which then cancels with the other.



Thank you! I had no idea how I didn't see that.

Quick Reply

Latest