BMath Bachelor of Mathematics Differential Equations

Question 1

What is the order of the differential equation d²y/dx² + 3 dy/dx + 2y = 0?

Accepted Answer

2

Answer

1

Answer

3

Answer

0

Question 2

The general solution of dy/dx = ky is:

Accepted Answer

y = Ce^(kx)

Answer

y = kx + C

Answer

y = Cx^k

Answer

y = k ln x + C

Question 3

Which method is used to find a particular solution of a nonhomogeneous linear ODE?

Accepted Answer

Method of undetermined coefficients

Answer

Separation of variables

Answer

Euler's method

Answer

Wronskian method

Question 4

For the IVP dy/dx = f(x, y), y(x₀) = y₀, Euler's method approximates y(x₀ + h) as:

Accepted Answer

y₀ + h·f(x₀, y₀)

Answer

y₀ − h·f(x₀, y₀)

Answer

y₀·f(x₀, y₀)

Answer

y₀ + h²·f(x₀, y₀)

Question 5

The Wronskian W(y₁, y₂) of two solutions is used to determine:

Accepted Answer

Whether the solutions are linearly independent

Answer

The particular solution of the ODE

Answer

The eigenvalues of the system

Answer

The order of the ODE

Question 6

The characteristic equation of y'' − 5y' + 6y = 0 is:

Accepted Answer

r² − 5r + 6 = 0

Answer

r² + 5r − 6 = 0

Answer

r² + 5r + 6 = 0

Answer

r − 5r² + 6 = 0