Differential Equations Class 12 Mcq Test (120901)

What does the constant "C" represent in the general solution of a linear differential equation?

a) The initial condition of the differential equation

b) The particular solution of the differential equation

c) The order of the differential equation

d) The degree of the differential equation

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 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

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

a) Zero

b) One

c) Two

d) Undefined

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

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 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

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