1.
Who invented differential equations?
Correct Answer
A. Isaac Newton
Explanation
Isaac Newton is credited with inventing differential equations. As a mathematician and physicist, Newton made significant contributions to the field of calculus, which is essential for understanding and solving differential equations. He developed the fundamental principles and techniques for solving these equations, revolutionizing the study of mathematics and its applications to physics and engineering. Newton's work laid the foundation for modern differential equations and their wide-ranging applications in various scientific disciplines.
2.
How many types of variations, are considered as the main ones when it comes to differential equations?
Correct Answer
B. Six
Explanation
There are six main types of variations when it comes to differential equations.
3.
What is a delay differential equation?
Correct Answer
D. It's a function of a single variable also called time.
Explanation
A delay differential equation is a type of differential equation where the derivative of the unknown function depends not only on its current value, but also on its past values. In other words, it involves a time delay in the equation. Therefore, it can be described as a function of a single variable, which is time.
4.
In what discipline is the Verhulst equation used?
Correct Answer
B. In Biology
Explanation
The Verhulst equation is a mathematical model used in population dynamics, specifically in biology. It is a differential equation that describes the growth of a population over time, taking into account factors such as birth rate, death rate, and carrying capacity. The equation was developed by Belgian mathematician Pierre FranÃ§ois Verhulst in the 19th century and has since been widely used in the field of biology to study and understand population growth and dynamics.
5.
In what discipline are differential equations used to measure chemical reactions?
Correct Answer
C. In Chemistry
Explanation
Differential equations are used in chemistry to measure chemical reactions because they provide a mathematical framework for describing the rates at which reactants are transformed into products. These equations help to model and predict how concentrations of reactants and products change over time, allowing chemists to understand and control the reaction processes. By solving these equations, chemists can determine reaction rates, equilibrium constants, and other important parameters that are crucial in studying and manipulating chemical reactions.
6.
Which of the differential equations are solvable?
Correct Answer
B. The simplest differential equations.
Explanation
The simplest differential equations are solvable because they involve only basic mathematical operations and can be easily solved using various techniques such as separation of variables, integrating factors, or substitution. These equations typically have a single independent variable and a single dependent variable, making them easier to manipulate and solve compared to more complex or compounded differential equations.
7.
Which invention gave birth to these types of equations?
Correct Answer
C. Calculus
Explanation
Calculus is the correct answer because it is a branch of mathematics that deals with rates of change and accumulation. It was developed by Sir Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century. Calculus is used to model and solve problems in various fields, including physics, engineering, economics, and biology. Equations derived from calculus are used to describe and analyze phenomena in these fields, making it an essential tool for understanding the natural world.
8.
How many kinds of differential equations were listed by Newton?
Correct Answer
B. 3
Explanation
Newton listed three kinds of differential equations. The question asks for the number of kinds of differential equations listed by Newton, and the correct answer is 3.
9.
In what year did these types of differential equations first appear?
Correct Answer
C. In 1671
Explanation
In 1671, these types of differential equations first appeared.
10.
Which equation theory was simplified by Leibniz?
Correct Answer
A. Jacob Bernoulli equation
Explanation
Leibniz simplified the Jacob Bernoulli equation.