Any thoughts on how to to any of these!! (I'm sorry if i'm insulting you but y' = dy/dx, etc!)(adsbygoogle = window.adsbygoogle || []).push({});

1)Find a continous solution with continous first derivative of the system:

y'' + 2y' + 2y = sin x + f(x)

subject to y(-pi/2)=y(pi)=0, where

f(x)= 0 (x<or= 0)

=x^2 (x>0)

2)You may ignore the first bits (i am including them just incase they're relavent for the last bit)

Verify y = x+1 is a soln of

(x^2-1)y'' + (x+1)y' - y = 0 *

Writing y=(x+1)u show that u'=0

hence show the gen soln of * is

y=K[0.25(x+1)ln((x-1)/(x+1))-0.5] + K'(x+1)

where K and K' are arbitary constants.

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# Two questions on differential equations

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