given y1 find y2 (Differential Equations) (3x-1)y''-(3x+2)y'-(6x-8)y=0 and y1=e^(2x)

given y1 find y2 (Differential Equations)

(3x-1)y''-(3x+2)y'-(6x-8)y=0 and y1=e^(2x)

Expert Solution

Colby Messinger answered 3 months ago

You can verify that the differential equation: −7x2y′′−14x(x−1)y′+14(x−1)y=0−7x2y″−14x(x−1)y′+14(x−1)y=0, x>0x>0 has solutions y1=3xy1=3x and y2=5xexp(−2x)y2=5xexp⁡(−2x). Compute the...

You can verify that the differential equation: −7x2y′′−14x(x−1)y′+14(x−1)y=0−7x2y″−14x(x−1)y′+14(x−1)y=0, x>0x>0 has solutions y1=3xy1=3x and y2=5xexp(−2x)y2=5xexp⁡(−2x). Compute the Wronskian WW between y1y1 and y The solutions y1y1 and y2y2 form a fundamental set of solutions because there is a point x0x0 where W(x0)≠0W(x0)≠0

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