Which of the following is one of the criterions for linearity of an equation?a)The dependent variable and its derivatives should be of second orderb)The dependent variable and its derivatives should not be of same orderc)Each coefficient does not depend on the independent variabled)Each coefficient depends only on the independent variableCorrect answer is option 'D'. Can you explain this answer?

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Which of the following is one of the criterions for linearity of an equation?

a)
The dependent variable and its derivatives should be of second order
b)
The dependent variable and its derivatives should not be of same order
c)
Each coefficient does not depend on the independent variable
d)
Each coefficient depends only on the independent variable

Correct answer is option 'D'. Can you explain this answer?

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Which of the following is one of the criterions for linearity of an eq...

Linearity of an equation:

Linearity refers to the property of an equation where the dependent variable and its derivatives have a linear relationship with the independent variable. In other words, a linear equation is one that can be expressed in the form of a straight line on a graph.

Criterion for linearity:

The criterion for linearity of an equation is that each coefficient in the equation depends only on the independent variable. This means that the coefficients should not be dependent on the dependent variable or any of its derivatives.

Explanation:

Linearity is determined by the relationship between the dependent variable and the independent variable. If an equation is linear, it means that the dependent variable and its derivatives have a linear relationship with the independent variable.

In a linear equation, each coefficient represents the slope or rate of change of the dependent variable with respect to the independent variable. These coefficients determine how the dependent variable and its derivatives vary with changes in the independent variable.

If each coefficient in the equation depends only on the independent variable, it implies that the rate of change of the dependent variable and its derivatives is constant and does not depend on the values of the dependent variable or its derivatives. This is a characteristic of a linear equation.

On the other hand, if the coefficients depend on the dependent variable or its derivatives, the rate of change of the dependent variable and its derivatives will vary with changes in the values of the dependent variable or its derivatives. This violates the criterion for linearity.

Therefore, the correct criterion for linearity of an equation is that each coefficient depends only on the independent variable (option D). This ensures that the equation represents a linear relationship between the dependent variable and the independent variable.

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Which of the following is one of the criterions for linearity of an eq...

The two criterions for linearity of an equation are:

The dependent variable y and its derivatives are of first degree.
Each coefficient depends only on the independent variable

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