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

What is the order of the differential equation 3 d2y ⎛ dy ⎞ + 5⎜ ⎟ − 4 y 2 dx ⎝ dx ⎠?

  • Third order
  • First order
  • Second order (correct)
  • Fourth order
  • Which type of differential equation involves partial derivatives of one or more dependent variables with respect to two or more independent variables?

  • First order differential equation
  • Partial differential equation (correct)
  • Second order differential equation
  • Ordinary differential equation
  • In the context of differential equations, what does IVP stand for?

  • Internal Value Problem
  • Integral Value Problem
  • Intrinsic Variable Problem
  • Initial Value Problem (correct)
  • What does a general solution of a differential equation contain?

    <p>All solutions for all constants</p> Signup and view all the answers

    What type of 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 order of a differential equation represent?

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

    What condition must the function and its derivatives satisfy for the solution of a general differential equation to be defined over some interval?

    <p>The function must be continuous for all t in the interval</p> Signup and view all the answers

    What is the main focus of the course MTH401?

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

    Which type of equation involves the highest power of the variable?

    <p>Cubic equation</p> Signup and view all the answers

    What is the solution of the differential equation dy/dx = 1/x?

    <p>$y=\ln x$</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 of integration involves breaking down a complicated integral into simpler ones?

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

    Which type of differential equations are mostly old concepts presented differently?

    <p>Differential Equations</p> Signup and view all the answers

    In the differential equation dy/dx - 5y/(y-x) = 0, what is the main problem?

    <p>$dy/dx$ and $y/(y-x)$ are inversely related</p> Signup and view all the answers

    What is the standard way to represent a second derivative in differential equations?

    <p>$d^2y/dx^2$</p> Signup and view all the answers

    In the equation ∂u/∂v + ∂y/∂x = x + y, what does it represent?

    <p>Partial Derivatives</p> Signup and view all the answers

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