16 Questions
What is the order of the differential equation 3 d2y ⎛ dy ⎞ + 5⎜ ⎟ − 4 y 2 dx ⎝ dx ⎠?
Second order
Which type of differential equation involves partial derivatives of one or more dependent variables with respect to two or more independent variables?
Partial differential equation
In the context of differential equations, what does IVP stand for?
Initial Value Problem
What does a general solution of a differential equation contain?
All solutions for all constants
What type of equation involves only ordinary derivatives of one or more dependent variables with respect to a single variable?
Ordinary Differential Equation
What does the order of a differential equation represent?
The highest derivative appearing in the equation
What condition must the function and its derivatives satisfy for the solution of a general differential equation to be defined over some interval?
The function must be continuous for all t in the interval
What is the main focus of the course MTH401?
Calculus
Which type of equation involves the highest power of the variable?
Cubic equation
What is the solution of the differential equation dy/dx = 1/x?
$y=\ln x$
What is the reverse process of differentiation called?
Integration
Which method of integration involves breaking down a complicated integral into simpler ones?
By parts
Which type of differential equations are mostly old concepts presented differently?
Differential Equations
In the differential equation dy/dx - 5y/(y-x) = 0, what is the main problem?
$dy/dx$ and $y/(y-x)$ are inversely related
What is the standard way to represent a second derivative in differential equations?
$d^2y/dx^2$
In the equation ∂u/∂v + ∂y/∂x = x + y, what does it represent?
Partial Derivatives
Test your knowledge of background concepts including linear, quadratic, and cubic equations, systems of linear equations, differential operators, and anti-derivatives. Also, assess your understanding of the connections with algebra, trigonometry, calculus, and various functions.
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