The method of separation of variables is used to solve which type of differential equations?

a) Homogeneous differential equations

b) Linear differential equations

c) Second-order differential equations

d) First-order differential equations

The general solution of a homogeneous differential equation of the form \(\frac{dy}{dx} + p(x)y = 0\) is given by:

a) \(y = Ce^(∫p(x)dx)\)

b) \(y = Ce^(-∫p(x)dx)\)

c) \(y = C∫p(x)dx\)

d) \(y = \frac{C}{x}\)

What is the order of the differential equation \(\frac{d^2y}{dx^2} + \frac{dy}{dx} + y = 0\)?

a) First order

b) Second order

c) Third order

d) Fourth order

What is the degree of the differential equation \(\frac{d^2y}{dx^2} + \frac{dy}{dx} + y = 0\)?

a) Zero

b) One

c) Two

d) Undefined

The Integrating Factor of differential equation of the form \(\frac{dy}{dx} + py = q\) is given by:

a) \(y = e^(-∫p dx)\)

b) \(y = e^(∫p dx)\)

c) \(y = e^(-∫p dy)\)

d) \(y = e^(∫p dy)\)

What is the general solution of a differential equation?

a) A solution that satisfies the equation for any given initial condition

b) A solution that satisfies the equation for a specific initial condition

c) A solution that satisfies the equation for only certain values of the independent variable

d) A solution that satisfies the equation for all values of the independent variable

What is the solution of the differential equation \(\frac{dy}{dx} = 3x^2\)?

a) \(y = x^3 + C\)

b) \(y = x^3 + 3x + C\)

c) \(y = 3x^2 + C\)

d) \(y = 2x^3 + C\)

What is the degree of the differential equation \(\frac{dy}{dx} + p(x)y = q(x)\)?

a) Zero

b) One

c) Two

d) Undefined

Which method is used to solve homogeneous differential equations of first order and first degree?

a) Separation of variables

b) Method of undetermined coefficients

c) Variation of parameters

d) Substitution method

What is the order of the differential equation \(\frac{dy}{dx} + p(x)y = q(x)\)?

a) First order

b) Second order

c) Third order

d) Higher order