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  • 09-08-2021
  • Mathematics
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5. Solve the differential equation y" - 5y "+7y'-3y=0.​

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LammettHash
LammettHash LammettHash
  • 09-08-2021

The differential equation

y''' - 5y'' + 7y' - 3y = 0

has characteristic equation

r ³ - 5r ² + 7r - 3 = (r - 3) (r - 1)² = 0

with roots at r = 3 and r = 1 (with multiplicity 2), so that the characteristic solution to the DE is

y = C₁ exp(3x) + C₂ exp(x) + C₃ x exp(x)

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