- #1
captainjack2000
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- 0
1. The question asks me to show that e^x is a solution of xy'' - (2x+1)y' + (x+1)y=0 and find the general solution.
2. I managed to simplify the equation to u''xe^(x) - u'e^(x) = 0 by letting y=ue^(x) and finding the differentials and substituting them in.
I've then let z=u dz/du=u' and d^2z/du^2 = u''
so I get xe^(x)(d^2z/du^2) - e^(x)dz/du = 0
How would I solve this?
2. I managed to simplify the equation to u''xe^(x) - u'e^(x) = 0 by letting y=ue^(x) and finding the differentials and substituting them in.
I've then let z=u dz/du=u' and d^2z/du^2 = u''
so I get xe^(x)(d^2z/du^2) - e^(x)dz/du = 0
How would I solve this?