- #1
fudge
Any thoughts on how to to any of these! (I'm sorry if I'm insulting you but y' = dy/dx, etc!)
1)Find a continuous solution with continuous 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.
1)Find a continuous solution with continuous 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.