Is (1+y^2) d^2y/dt^2 + t dy/dt + y = et a Linear Equation?

Thread starter patrickbotros
Start date Mar 6, 2015
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Linear Linear equation

In summary, a linear equation is an algebraic equation with constants and variables that can be graphed as a straight line. To determine if an equation is linear, it must be in the form y = mx + b, with a constant rate of change. The difference between linear and non-linear equations is that the slope of a linear equation is constant, while a non-linear equation's slope varies and is graphed as a curve. A linear equation can have more than one variable as long as it follows the y = mx + b form. In science, linear equations are used to model real-world situations, make predictions, and analyze data in fields such as physics, chemistry, and biology.

Mar 6, 2015

patrickbotros

(1+y²) d²y/(dt²) + t dy/dt +y = e^t

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Mar 6, 2015

leonita

I think its not linear, there's y squared

Mar 7, 2015

shubhdeep

No, it's not.

Mar 7, 2015

HallsofIvy

Science Advisor

Homework Helper

It is not because, as Leonita said, it has a non-linear function of the dependent variable, y.

1. What is a linear equation?

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. The graph of a linear equation is a straight line.

2. How can I tell if an equation is linear?

An equation is linear if it can be written in the form y = mx + b, where m and b are constants and x is a variable. If the equation is in this form, it is linear. If it cannot be written in this form, it is not linear.

3. What is the difference between linear and non-linear equations?

A linear equation has a constant rate of change, meaning that the slope of the line is always the same. A non-linear equation does not have a constant rate of change, and the graph of the equation is a curve rather than a straight line.

4. Can a linear equation have more than one variable?

Yes, a linear equation can have more than one variable. However, it must still follow the form y = mx + b, where m and b are constants and y and x are variables. The graph of a linear equation with more than one variable will be a line in a higher-dimensional space.

5. How are linear equations used in science?

Linear equations are used in many scientific fields, including physics, chemistry, and biology. They can be used to model real-world situations, make predictions, and analyze data. For example, in physics, linear equations are used to describe the motion of objects and in chemistry, they are used to calculate reaction rates.