If = ae2x + be-x, then show that d2y/dx2 − dy/dx - 2y = 0.

1.	If = ae2x + be-x, then show that d2y/dx2 − dy/dx - 2y = 0.
Answer» y = ae^2x + be^-x .........(1) dy/dx = 2ae^2x - be^-x .........(2) d²y/dx² = 4ae^2x+ be^-x...........(3) putting values on LHS = d²y/dx² - dy/dx - 2y = (4ae^2x + be^-x) - (2ae^2x- be^-x) - 2(ae^2x + be^-x) = 4ae^2x + be^-x- 2ae^2x+ be^-x - 2ae^2x - 2be^-x ^{= 0}

Answer»

y = ae^2x + be^-x .........(1)

dy/dx = 2ae^2x - be^-x .........(2)

d²y/dx² = 4ae^2x+ be^-x...........(3)

putting values on LHS

= d²y/dx² - dy/dx - 2y

= (4ae^2x + be^-x) - (2ae^2x- be^-x) - 2(ae^2x + be^-x)

= 4ae^2x + be^-x- 2ae^2x+ be^-x - 2ae^2x - 2be^-x

^{= 0}

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If = ae2x + be-x, then show that d2y/dx2 − dy/dx - 2y = 0.

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