Question

It can be helpful to classify a differential equation, so that we can predict the techniques that might help us to find a function which solves the equation. Two classifications are the order of the equation -- (what is the highest number of derivatives involved) and whether or not the equation is linear . Linearity is important because the structure of the the family of solutions to a linear equation is fairly simple. Linear equations can usually be solved completely and explicitly. Determine whether or not each equation is linear:

Answer 1

The equations are not given but the clue to your answer is given below:

Explanation:

So the question above talks generally about differential equations (equations whose derivatives can be found) and then describes them thus - the order of a differential equation and the linearity status of a differential equation.

To determine whether or not each of the absent equations is linear, check for the following characteristics of linearity:

1. The maximum number or power that any variable in a linear equation is raised to is 1.

Example: 2x² + 6y = 43y is NOT a linear equation because some or all (in this case, variable x) of the variables in it are raised to a power greater than 1. Variable x is raised to the power of 2.

2. An equation (a linear equation, in this case) contains an 'equal to' sign. This is the reason why it's called an equation. There is a mathematical expression on each side of the equal to sign. Take note of this, just incase one of the options in your question has no equal to sign.

Example: 2x + 6y is NOT a linear equation. It is a linear expression. It contains no equal to sign that compares two distinct mathematical expressions.

3. A linear equation usually has not more than two variables. It is not complex or difficult to solve.

Example: 2x + 6y = 43z is NOT a linear equation.