Differential Equations

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What is the order of the differential equation dy/dx = 1 + x + y?

3

2

1 (correct)

4

Which of the following is an example of a linear differential equation?

dy/dx = x^2 + y^2

dy/dx = 1 + x + y

dy/dx = xy

x d^2y/dx^2 + y = 0 (correct)

What is the purpose of formulating a problem as a differential equation?

To find the approximate solution

To solve the problem analytically

To convert the problem into a mathematical model (correct)

To visualize the problem graphically

Which of the following is an example of a higher order differential equation?

d^2y/dx^2 + 4y = 0 Signup and view all the answers

What is the significance of solving differential equations in physics and engineering?

To solve practical problems Signup and view all the answers

What is a characteristic of a non-linear differential equation?

Its degree is more than one Signup and view all the answers

What is the purpose of an integrating factor in a linear differential equation of first order?

To make the left-hand side of the differential equation an exact differential Signup and view all the answers

What is the general form of a linear differential equation of first order?

dy/dx + Py = Q Signup and view all the answers

Which of the following is an example of a linear differential equation?

dy/dx + xy = x^3 Signup and view all the answers

What is the name of the factor that is used to solve a linear differential equation of first order?

Integrating factor Signup and view all the answers

What is the general method used to solve the differential equation dz/dx = f(z,x)?

Separation of variables Signup and view all the answers

What is the integrating factor (I.F.) for the differential equation dz/dx + P(z)x = Q(z), where P(z) and Q(z) are functions of z?

e^(∫P(z)dx) Signup and view all the answers

What is the application of differential equations in physics?

To define physical laws and quantities Signup and view all the answers

What is the order of the differential equation dz/dx + (1/x)z = 2?

First order Signup and view all the answers

What is the general solution of the differential equation dz/dx = z/2, where z is a function of x?

z = e^(x/2) + c Signup and view all the answers

What is the definition of a differential equation?

An equation involving independent variable x, dependent variable y and the differential coefficients Signup and view all the answers

What is the order of the differential equation dy/dx + xy = cot(x)?

1 Signup and view all the answers

What are the two important aspects of differential equations?

Formulating a problem as a differential equation and how to solve it Signup and view all the answers

What is true about the order of a differential equation?

It is always a positive integer Signup and view all the answers

What is the purpose of differential equations in physics and engineering?

To model various phenomena Signup and view all the answers

What is the condition for a differential equation to be non-linear?

The degree of the differential equation is more than one. Signup and view all the answers

What is the purpose of the integrating factor in a linear differential equation of first order?

To make the left-hand side of the differential equation an exact differential. Signup and view all the answers

What is the result of multiplying both sides of a linear differential equation of first order by the integrating factor?

The left-hand side becomes an exact differential. Signup and view all the answers

What is the general form of the solution of a linear differential equation of first order?

ye^(∫Pdx) = Qe^(∫Pdx) + C Signup and view all the answers

Which of the following is not a characteristic of a non-linear differential equation?

The differential equation is of the first order. Signup and view all the answers

What is the general form of the solution of the differential equation d^2y/dx^2 = f(x)?

y = ∫∫F(x)dx^2 + c1x + c2 Signup and view all the answers

If dy/dx = f(x) is a differential equation, what is the general form of its solution?

y = ∫f(x)dx + c1 Signup and view all the answers

What is the method used to solve the differential equation dy/dx = f(x) + c1?

Direct integration Signup and view all the answers

If d^2y/dx^2 = -1 is a differential equation, what is its solution?

y = -x^2 + c1x + c2 Signup and view all the answers

What is the characteristic of a differential equation that can be written in the form dy/dx = f(x)g(y)?

It is a separable differential equation Signup and view all the answers

Differential Equations

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Questions and Answers

What is the order of the differential equation dy/dx = 1 + x + y?

Which of the following is an example of a linear differential equation?

What is the purpose of formulating a problem as a differential equation?

Which of the following is an example of a higher order differential equation?

What is the significance of solving differential equations in physics and engineering?

What is a characteristic of a non-linear differential equation?

What is the purpose of an integrating factor in a linear differential equation of first order?

What is the general form of a linear differential equation of first order?

Which of the following is an example of a linear differential equation?

What is the name of the factor that is used to solve a linear differential equation of first order?

What is the general method used to solve the differential equation dz/dx = f(z,x)?

What is the integrating factor (I.F.) for the differential equation dz/dx + P(z)x = Q(z), where P(z) and Q(z) are functions of z?

What is the application of differential equations in physics?

What is the order of the differential equation dz/dx + (1/x)z = 2?

What is the general solution of the differential equation dz/dx = z/2, where z is a function of x?

What is the definition of a differential equation?

What is the order of the differential equation dy/dx + xy = cot(x)?

What are the two important aspects of differential equations?

What is true about the order of a differential equation?

What is the purpose of differential equations in physics and engineering?

What is the condition for a differential equation to be non-linear?

What is the purpose of the integrating factor in a linear differential equation of first order?

What is the result of multiplying both sides of a linear differential equation of first order by the integrating factor?

What is the general form of the solution of a linear differential equation of first order?

Which of the following is not a characteristic of a non-linear differential equation?

What is the general form of the solution of the differential equation d^2y/dx^2 = f(x)?

If dy/dx = f(x) is a differential equation, what is the general form of its solution?

What is the method used to solve the differential equation dy/dx = f(x) + c1?

If d^2y/dx^2 = -1 is a differential equation, what is its solution?

What is the characteristic of a differential equation that can be written in the form dy/dx = f(x)g(y)?

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