Differential Equations
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Questions and Answers

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?

<p>d^2y/dx^2 + 4y = 0 (D)</p> Signup and view all the answers

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

<p>To solve practical problems (B)</p> Signup and view all the answers

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

<p>Its degree is more than one (D)</p> Signup and view all the answers

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

<p>To make the left-hand side of the differential equation an exact differential (B)</p> Signup and view all the answers

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

<p>dy/dx + Py = Q (B)</p> Signup and view all the answers

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

<p>dy/dx + xy = x^3 (C)</p> 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?

<p>Integrating factor (C)</p> Signup and view all the answers

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

<p>Separation of variables (D)</p> 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?

<p>e^(∫P(z)dx) (D)</p> Signup and view all the answers

What is the application of differential equations in physics?

<p>To define physical laws and quantities (D)</p> Signup and view all the answers

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

<p>First order (D)</p> 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?

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

What is the definition of a differential equation?

<p>An equation involving independent variable x, dependent variable y and the differential coefficients (B)</p> Signup and view all the answers

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

<p>1 (C)</p> Signup and view all the answers

What are the two important aspects of differential equations?

<p>Formulating a problem as a differential equation and how to solve it (B)</p> Signup and view all the answers

What is true about the order of a differential equation?

<p>It is always a positive integer (C)</p> Signup and view all the answers

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

<p>To model various phenomena (C)</p> Signup and view all the answers

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

<p>The degree of the differential equation is more than one. (D)</p> Signup and view all the answers

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

<p>To make the left-hand side of the differential equation an exact differential. (B)</p> 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?

<p>The left-hand side becomes an exact differential. (B)</p> Signup and view all the answers

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

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

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

<p>The differential equation is of the first order. (B)</p> Signup and view all the answers

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

<p>y = ∫∫F(x)dx^2 + c1x + c2 (A)</p> Signup and view all the answers

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

<p>y = ∫f(x)dx + c1 (B)</p> Signup and view all the answers

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

<p>Direct integration (A)</p> Signup and view all the answers

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

<p>y = -x^2 + c1x + c2 (A)</p> 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)?

<p>It is a separable differential equation (C)</p> Signup and view all the answers

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