What is the perpose of diffential equations?

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We were told to eleminate the constants using differentiation, and substitute the values of the constants in the original equation. I want to know why it is done so.


The purpose of Algebra is to make it easy to state a mathematical relationship and its equation by using letters of the alphabet or other symbols to represent entities as a form of shorthand. Algebra then allows you to substitute values in order to solve the equations for the unknown quantities.

There are numerous mathematical relationships that have been established in science, finance and other areas. Examples include the relationship between force and acceleration, conversion of centimeters to inches, and determining the payments on a loan with a given interest rate. These relationships are stated as equations.

Algebra allows you to use letters of the alphabet or other symbols to represent objects and numbers. This makes it more convenient

You can state a physical equation by using letters to represent the elements of the equation. For example, force equals mass times acceleration.

Algebra allows you to use letters of the alphabet to represent objects, number, or expressions. Numbers can be constants or variables.

The best way to explain how a relationship can be stated with letters is to provide some examples.

Example of loan payments

The amount of interest you pay on a loan is equal to the interest rate times the money owed. Thus, the equation is:

I = r * m


  • I = amount of interest
  • r = interest rate
  • m = money owed
  • * is the multiplication sign

The letters Ir and m are called variables in the equation, since they can vary depending on what value you give them.

Gravity equation

In Physics, the gravity equation is:

F = m*g


  • F is the force pulling an object toward the ground
  • m is the mass of the object
  • g is the acceleration due to gravity

g is a constant, since its value does not change, while F and m are variables.

The primary purpose of Algebra is to allow you to substitute letters for the names of items in a relationship, thus creating an equation. Then you can substitute in values to solve for an item. You can manipulate the equation to put it in terms of one of the variables.


Can you give an example problem you had to solve? This is too vague for us to be able to help.