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second order differential equations watch

1. I know I have done this question before but I can't find / remember it:

2nd order differential equation
a(d2y/dx2) + b(dy/dx) +cy = 0

show (by substitution) that if y1 and y2 satisfy above equation then so does y = Ay1 + By2

any pointers?
2. well quite clearly you need to find dy/dx and d2y/dx2 and sub them in.

do that and see if you can figure it out
3. If y = Ay1 + By2, then what is dy/dx (in therms of dy1/dx and dy2/dx)? And dy2/dx2? So, sub in, separate out, and you're done.
4. (Original post by bonbon)
I know I have done this question before but I can't find / remember it:

2nd order differential equation
a(d2y/dx2) + b(dy/dx) +cy = 0

show (by substitution) that if y1 and y2 satisfy above equation then so does y = Ay1 + By2

any pointers?
Hint: y' = Ay1' + By2' and y'' = Ay1'' + By2'', substitute them into the differential equation along with y and use the fact that both y1 and y2 satisfy the differential equation
5. ok thanks everyone... i'll have a go

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