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well, an equation with one variable is a one step equation and an equation with more than 2 variables is a multi-step equation
ordinary differential equation is obtained only one independent variable and partial differential equation is obtained more than one variable.
-- If the equation has only one variable (like 'x' or 'y'), and the only power of the variable anywhere in the equation is '1', then the equation has one solution. -- If the variable appears raised to powers higher than '1', then there are as many solutions as the highest power of the variable. -- If the equation has two or more variables, then there are an infinite number of solutions.
Equations can be classified according to the highest power of the variable. Since the highest power of the variable in a linear equation is one, it is also called a first-order equation.
When an equation has a variable in it (only one), then there are only certainvalues the variable can have that will make the equation a true statement."Solving" the equation means finding those values for the variable.