Differential Equations (MTH401) VU Lecture#1 Quiz
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Questions and Answers

What type of differential equation involves partial derivatives of one or more dependent variables with respect to two or more independent variables?

  • Mass-Spring System Equation
  • Partial Differential Equation (correct)
  • Logistic Differential Equation
  • Ordinary Differential Equation

    • The order of a differential equation is defined as the order of the highest __________ appearing in the equation.

  • Derivative (correct)
  • Integral
  • Limit
  • Function

    • If an equation contains only ordinary derivatives of one or more dependent variables with respect to a single variable, it is known as a(n) ________.

  • Ordinary Differential Equation (correct)
  • Exponential Equation
  • Partial Differential Equation
  • Logistic Equation

    • A general solution to a differential equation contains ____________.

    <p>Infinite arbitrary constants</p> Signup and view all the answers

    In the context of differential equations, what does IVP stand for?

    <p>Initial Value Problem</p> Signup and view all the answers

    What type of differential equation involves only ordinary derivatives of one or more dependent variables with respect to a single variable?

    <p>Ordinary Differential Equation</p> Signup and view all the answers

    What does the logistic equation p’ = ap – bp^2 represent?

    <p>Logistic Differential Equation</p> Signup and view all the answers

    What are the two types of problems associated with differential equations?

    <p>Initial Value Problem and Boundary Value Problem</p> Signup and view all the answers

    What does a general solution to a differential equation represent?

    <p>All possible solutions using arbitrary constants</p> Signup and view all the answers

    What is the order of an equation determined by?

    <p>The highest derivative appearing in the equation</p> Signup and view all the answers

    What is the primary focus of the course Differential Equations (MTH401)?

    <p>Differentiation and Integration</p> Signup and view all the answers

    Which mathematical concept is NOT part of the background for Differential Equations (MTH401)?

    <p>Matrices and Determinants</p> Signup and view all the answers

    What is the solution method for the equation ax+by+c=0 in a system of linear equations?

    <p>$x = \frac{-by-c}{a}$</p> Signup and view all the answers

    Which function's differentiation results in the equation dy/dx = 1/x?

    <p>Logarithmic Function</p> Signup and view all the answers

    What theorem is related to finding higher order derivatives through successive differentiation?

    <p>Leibnitz Theorem</p> Signup and view all the answers

    What is the reverse process of differentiation called?

    <p>Integration</p> Signup and view all the answers

    Which method involves expressing a function as a product of two functions and integrating by parts?

    <p>By Parts</p> Signup and view all the answers

    Which method involves expressing a function as a product of two functions and integrating by parts?

    <p>By Parts</p> Signup and view all the answers

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