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

The order of a differential equation is the highest derivative present; here it is d²y/dx², which is second order.

Question 2

The general solution of dy/dx = ky is:

Accepted Answer

y = Ce^(kx)

Answer

Separating variables: dy/y = k dx, integrating gives ln|y| = kx + C₀, so y = Ce^(kx).

Question 3

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

Accepted Answer

Method of undetermined coefficients

Answer

The method of undetermined coefficients guesses a particular solution form matching the forcing function and solves for the coefficients.

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

Euler's method uses the tangent line approximation: y₁ ≈ y₀ + h·f(x₀, y₀), stepping forward by step size h.

Question 5

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

Accepted Answer

Whether the solutions are linearly independent

Answer

If W(y₁, y₂) ≠ 0 on an interval, then y₁ and y₂ are linearly independent and form a fundamental set of solutions.

BMath Bachelor of Mathematics Practice Test