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Solve the differential equation y'' - 5y' + 6y = 0.

Practice Questions

Q1
Solve the differential equation y'' - 5y' + 6y = 0.
  1. y = C1 e^(2x) + C2 e^(3x)
  2. y = C1 e^(3x) + C2 e^(2x)
  3. y = C1 e^(x) + C2 e^(2x)
  4. y = C1 e^(2x) + C2 e^(x)

Questions & Step-by-Step Solutions

Solve the differential equation y'' - 5y' + 6y = 0.
  • Step 1: Identify the given differential equation: y'' - 5y' + 6y = 0.
  • Step 2: Write the characteristic equation by replacing y'' with r^2, y' with r, and y with 1: r^2 - 5r + 6 = 0.
  • Step 3: Factor the characteristic equation: (r - 2)(r - 3) = 0.
  • Step 4: Set each factor equal to zero to find the roots: r - 2 = 0 gives r = 2, and r - 3 = 0 gives r = 3.
  • Step 5: Write the general solution using the roots found: y = C1 e^(2x) + C2 e^(3x), where C1 and C2 are constants.
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