[oceane]

Hello

Edexcel exercise 6e pg 110 question 7:

x (d2y/dx2) - 2 (dy/dx) + x=0 Using the substitution dy/dx=v

Not sure how to go about this one, have played around with it but don't really know what I'm looking for so if you can see it please tell me!

Cheers

[Fermat]

use the substitution to get a 1st order d.e.

[Gaz031]

Originally Posted by oceane

Hello

Edexcel exercise 6e pg 110 question 7:

x (d2y/dx2) - 2 (dy/dx) + x=0 Using the substitution dy/dx=v

Not sure how to go about this one, have played around with it but don't really know what I'm looking for so if you can see it please tell me!

Cheers

dy/dx=v, d^2y/dx^2=dv/dx
xdv/dx-2v+x=0
dv/dx+v[-2/x]+1=0
dv/dx+v[-2/x]=-1
Integrating factor: e^INT(-2/x) dx = e^(-2lnx)=e^(lnx^-2)=x^-2=1/(x^2)
v/x^2=INT -1/x^2 dx
v/x^2=INT-x^-2 dx
v/x^2=x^-1+C
v=x+Cx^2
dy/dx=x+Cx^2
y=0.5x^2+Ax^3+B

[oceane]

Neat. Thanks to you both.