Solving Linear Second Order Homogeneous Differential Equations

What type of differential equations are discussed in the text?

• First-order linear differential equations

• Second-order linear differential equations

• Non-linear differential equations

• Partial differential equations

What are the coefficients in the quadratic equation used to solve homogeneous second-order linear differential equations?

• r, s, t

• m, n, p

• x, y, z

• a, b, c

What are the solutions when the roots of the quadratic equation are distinct?

• e^r1x, e^r2x

• r1, r2

• r1x, r2x

• r1e^x, r2e^x

What is the solution form when the roots of the quadratic equation are repeated?

• C1e^r1x, C2e^r2x

• C1e^rx, C2e^rx

• C1e^r1x, C2xe^r2x

• C1e^r1x, C2e^rx

What is the solution form when the roots of the quadratic equation are complex?

• C1e^(r1x)sin(r2x), C2e^(r1x)cos(r2x)

• C1e^(r1x), C2e^(r2x)

• C1e^(r1x)cos(r2x), C2e^(r1x)sin(r2x)

• C1cos(x), C2sin(x)

What is the solution to the equation y double prime + y prime - 6y = 0?

• C1e^(3x) + C2e^(-2x)

• C1e^(-3x) + C2e^(2x)

• C1e^(2x) + C2e^(-3x)

• C1e^(-2x) + C2e^(3x)

What is the solution to the equation y double prime - 8y prime + 16y = 0?

• C1e^(4x) + C2xe^(4x)

• C1e^(4x) + C2e^(4x)

• C1e^(-4x) + C2e^(-4x)

• C1e^(4x) + C2e^(-4x)