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Edexcel FP2 - 2nd order differentiation question

(a) Find the general solution of the differential equation
4(d2y/dy2) - (dy/dx) - 3y = x^2

[CF: Ae^((-3/4)x) + Be^x]

(b) Find the particular solution for which, x=0, y=3 and dy/dx = 5

according to the mark scheme, you start with y = px^2 + qx + r => y' = 2px + q, y'' = 2p

anyone know why you have to assume that equation for y? does it have anything to do with the x^2 in the original equation (implying a quadratic in y)?
(edited 13 years ago)
Original post by the maths guy
(a) Find the general solution of the differential equation
4(d2y/dy2) - (dy/dx) - 3y = x^2

[CF: Ae^((-3/4)x) + Be^x]

(b) Find the particular solution for which, x=0, y=3 and dy/dx = 5

according to the mark scheme, you start with y = px^2 + qx + r => y' = 2px + q, y'' = 2p

anyone know why you have to assume that equation for y? does it have anything to do with the x^2 in the original equation (implying a quadratic in y)?

Yes, that's what I'd imagine the reasoning to be. The RHS is a quadratic and having y as a quadratic will also give you a quadratic on the LHS.
Reply 2
Avatar for Mechie
Mechie
15
Original post by Farhan.Hanif93
Yes, that's what I'd imagine the reasoning to be.


When did you have your Cambridge interview btw?
Original post by davidmarsh01
When did you have your Cambridge interview btw?

The 8th.
Reply 4
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Slowbro93
20
Original post by davidmarsh01
When did you have your Cambridge interview btw?


Hey, how did your cam interview go?
Reply 5
Avatar for Mechie
Mechie
15
Original post by cpdavis
Hey, how did your cam interview go?


Yeah, the interview went pretty well actually, but the test was worse :s-smilie: Hope they liked me :p:
Reply 6
Avatar for the maths guy
the maths guy
OP
Original post by Farhan.Hanif93
Yes, that's what I'd imagine the reasoning to be. The RHS is a quadratic and having y as a quadratic will also give you a quadratic on the LHS.
so if the RHS was 3x, y would be ax + b?
and if 2, y = ax?

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