Solving Linear Second Order Homogeneous Differential Equation

Find the solution to the differential equation y'' - 4y' + 4y = 0 using the Auxiliary Equation method.

• y = c1*e^(2x) + c2*e^(2x)

• y = c1*e^(2x) + c2*x*e^(2x)

• y = c1*x*e^(2x) + c2*e^(2x)

• y = c1*e^(2x) + c2*x^2*e^(2x)

Solve the differential equation y'' + 9y = 0 using the Auxiliary Equation technique.

• y = c1*sin(9x) + c2*cos(9x)

• y = c1*cos(3x) + c2*sin(3x

• y = c1*cos(9x) + c2*sin(9x)

• y = c1*sin(3x) + c2*cos(3x

Determine the general solution to the differential equation y'' - 6y' + 9y = 0 by applying the Auxiliary Equation approach.

• y = c1 * e^(3x) + c2 * x * e^(3x)

• y = c1 * e^(4x) + c2 * x * e^(3x)

• y = c1 * e^(3x) + c2 * x^2 * e^(3x)

• y = c1 * e^(2x) + c2 * x * e^(3x)

Solve the differential equation y'' - 5y' + 6y = 0 by using the Auxiliary Equation method.

• y = c1*e^(4x) + c2*e^(5x)

• y = c1*e^(2x) + c2*e^(3x)

• y = c1*e^(x) + c2*e^(6x)

• y = c1*e^(2x) + c2*e^(4x)

Determine the general solution to the differential equation y'' - 3y' + 2y = 0 by applying the Auxiliary Equation approach.

• y = c1*e^(-x) + c2*e^(2x)

• y = c1*e^(2x) + c2*e^(-x)

• y = c1*e^(-x) + c2*x*e^(2x)

• y = c1*e^(x) + c2*e^(-2x)