d2y/dx2 + 4*dy/dx + 4y = 2cos2xor
d3y/dx3 -2*d2y/dx2 + dy/dx -2y = 12*sin2x
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Partial differential equations are mathematical equations that involve two or more independent variables, an unknown function, and partial derivatives of the unknown function. Even the explanation is confusing! If, however, anyone chooses to learn about PDE there are classes offered at any institution of higher learning.
A linear equation is defined as an equation that contains only the first power of the unknown quantity. For example, 5x - 3 = 7 where "x" is the unknown quantity is a linear equation. If an equation contains an unknown quantity having a higher power than 1, then the equation ceases to be a linear equation. For example, 3x2 + 5x + 7 = 0 is a non linear equation known as a quadratic equation, because the unknown quantity "x" has a power of 2. Similarly, equations containing unknowns with higher powers such as x3, x7, x12 are all non linear equations.
As an automotive engineer, I mostly use algebra, but I sometimes use geometry, statistics, and calculus. Some higher level research positions may use differential equations.
Calculus is higher than Algebra. There are also courses on Linear Algebra and Differential Equations that are higher than college Algebra. If you contact the Math department of any college they should be able to give you a specific answer as to what courses they correspond with and what a challenging math class would be.
The word linear means in a straight line. If the graph is a line, it is linear. Also, linear equations are of the first order; they contain a variable but not a square (or higher power) of a variable. If the equation contains x2 it is not linear.