Differential Equations Class 12 Mcq Test (120901)

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

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 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 \(\frac{d^2y}{dx^2} + \frac{dy}{dx} + y = 0\)?

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

What is the order of a differential equation?

a) The highest power of the derivative in the equation

b) The lowest power of the derivative in the equation

c) The sum of all powers of the derivative in the equation

d) The degree of the polynomial in the equation

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 degree of a differential equation is determined by:

a) The highest power of the derivative in the equation

b) The lowest power of the derivative in the equation

c) The sum of all powers of the derivative in the equation

d) The degree of the polynomial in the equation

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 particular solution of a linear differential equation requires:

a) Initial conditions to be specified

b) The order of the differential equation to be determined

c) The degree of the differential equation to be determined

d) The general solution of the differential equation to be found