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It is an equation in which one of the terms is the instantaneous rate of change in one variable, with respect to another (ordinary differential equation). Higher order differential equations could contain rates of change in the rates of change (for example, acceleration is the rate of change in the rate of change of displacement with respect to time). There are also partial differential equations in which the rates of change are given in terms of two, or more, variables.

Q: What is differential equations as it relates to algebra?

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Algebraic equations, trigenometric equations, linear equations, geometric equations, partial differential equations, differential equations, integrals to name a few.

There are many different formulas and equations for algebra.

The answer will depend on what kinds of equations: there are linear equations, polynomials of various orders, algebraic equations, trigonometric equations, exponential ones and logarithmic ones. There are single equations, systems of linear equations, systems of linear and non-linear equations. There are also differential equations which are classified by order and by degree. There are also partial differential equations.

Linear Algebra is a branch of mathematics that enables you to solve many linear equations at the same time. For example, if you had 15 lines (linear equations) and wanted to know if there was a point where they all intersected, you would use Linear Algebra to solve that question. Linear Algebra uses matrices to solve these large systems of equations.

expressions don't have an equal sign and equations do

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No. Differential equations come up in Calculus.

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We don't. We then learn trig, calculus, and then differential equations, and we use that.

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Arithmetic , algebra, some differential equations might occur in analysis.

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