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प्रश्न
Find the value of m so that the function y = emx solution of the given differential equation.
y” – 5y’ + 6y = 0
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उत्तर
Given y = emx ........(2)
Differentiating equation (2) w.r.t ‘x’, we get
`("d"y)/("d"x)` = ex. m
Again differentiating w.r.t ‘x’, we get
`("d"^2y)/("d"x^2)` = emx. m2
To find the value of m:
Given y” – 5y’ + 6y = 0
∵ y = emx
emx. m2 – 5memx + 6 emx 0, `("d"y)/("d"x)` = emx . m
emx[m2 – 5m + 6] = 0, `("d"^2y)/("d"x^2)` = emx. m2
m² – 5m + 6 = 0
(m – 2)(m – 3) = 0
∴ m = 2, 3
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