Is \rhoutt + EIuxxxx = 0 a Linear or Non-Linear Math Problem?

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In summary, the conversation discusses various equations and their linearity. The first equation, \rhoutt + EIuxxxx = 0, is determined to be linear by the fact that it can be expressed as L(u+v) = Lu + Lv. The second equation, ut - \alpha^2\nabla^2u = ru(M -u), is also determined to be linear by the same reasoning. The last equation, ut + (1-u)ux = 0, is not explicitly stated to be linear or non-linear, but the equation ux + exutt = sin(x) is determined to be non-linear due to the additional terms of uxy, uyy, and ux. The last equation, ut +
  • #1
squenshl
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I'm trying to see if [tex]\rho[/tex]utt + EIuxxxx = 0 is linear or non-linear where [tex]\rho[/tex], E and I are constants.

I got L(u+v) = [tex]\rho[/tex][tex]\delta[/tex]2u2/[tex]\delta[/tex]t2 + EI[tex]\delta[/tex]4u2/[tex]\delta[/tex]x4 + [tex]\rho[/tex][tex]\delta[/tex]2uv/[tex]\delta[/tex]t2 + EI[tex]\delta[/tex]4uv/[tex]\delta[/tex]x4 = Lu + Lv. Does this mean it's linear or is there more to do.
 
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  • #2


That is enough.
 
  • #3


Cheers.
What about this one then.
ut - [tex]\alpha^2[/tex][tex]\nabla^2[/tex]u = ru(M -u) where [tex]\alpha[/tex], r & M are constants.

ut - [tex]\alpha^2[/tex][tex]\nabla^2[/tex]u - ru(M -u) = 0
L(u+v+w) = ut(u+v+w) + [tex]\alpha^2[/tex][tex]\nabla^2[/tex]u(u+v+w) - ru(M-u)(u+v+w) = utt + [tex]\alpha^2[/tex][tex]\nabla^2[/tex]u2 - ru2(M-u) + utv + [tex]\alpha^2[/tex][tex]\nabla^2[/tex]uv - ruv(M-u) + utw + [tex]\alpha^2[/tex][tex]\nabla^2[/tex]uw - ruw(M-u) = Lu + Lv + Lw
 
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  • #4


Are these equation linear or non-linear?

ut + (1-u)ux = 0
uxx + exutt = sin(x)
uxx + uxy + uyy + ux = t2
 
  • #5


Someone help please.
 

FAQ: Is \rhoutt + EIuxxxx = 0 a Linear or Non-Linear Math Problem?

1. What is a "linearity math problem"?

A linearity math problem is a type of mathematical problem that involves linear equations, which are equations in the form of y = mx + b. These equations describe a straight line on a graph and can be used to solve various real-world problems.

2. How do I solve a linearity math problem?

To solve a linearity math problem, you first need to identify the linear equation involved. Then, you can use various methods such as substitution, elimination, or graphing to find the solution. It is important to follow the order of operations and simplify the equation as much as possible before solving for the unknown variable.

3. What are some common applications of linearity math problems?

Linearity math problems are commonly used in fields such as physics, economics, and engineering. They can be used to model and predict relationships between variables, such as distance and time, or cost and quantity.

4. Are there any shortcuts or tricks for solving linearity math problems?

Yes, there are some shortcuts and tricks that can be used to solve linearity math problems faster. These include using the slope-intercept form of a linear equation (y = mx + b), understanding the relationship between slope and direction of a line, and using the point-slope form of a linear equation (y - y1 = m(x - x1)). Practice and familiarizing yourself with these methods can help you solve linearity math problems more efficiently.

5. What is the importance of linearity in mathematics?

Linearity is an important concept in mathematics because it allows us to model and understand relationships between variables in a simple and straightforward way. It is also the basis for more complex mathematical concepts such as calculus and differential equations. Understanding linearity can also help us make predictions and solve real-world problems more accurately.

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