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1- y'=y
2- y'=x+3 (T&A)
3- y' = 4x^2 - 9
4- y' = y + x^3
5- y' = 2xy/lnx
6-  y'/y = x^5

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1- xy''-y'=0
2- y'' + 3y' = 2
3-  y"= y' * y + x^2 : non linear

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1-when y is a function of x
y'-y=x   non-homogeneous
y'-y=0 homogeneous

2- xy"+y'=x-3 non-homogenous
xy"'+y"=-x non- homogeneous (T&A)

3- 5y''' + 2y'' - 3y' + y=0 homogenous
y'-y = x + 5 non- homogeneous

4-
Homogenous:
Non-Homogenous:

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1- linear : xy'+y/ln(x) = sinx
non-linear : y y"= e^x
2-
linear: y'''+y''/2x+y-x = arctan(x)
non-linear: y'^5*y^3 = Ln lxl
3- linear: y' - ln(x)=0
4- non-linear: (y''(3x^2))/y' + y = x^2

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Partial Differ: ∂

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Add a list of Theorems and concepts you have learned on 1st order and 2nd order ODEs that might apply to nth order, too.

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Add a list of Theorems and concepts you have learned on 1st order and 2nd order ODEs that might apply to nth order, too.

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1- Wronskian

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4 - existence and uniqueness THM for linear homogenous ODEs

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5. We can use the idea of Linear operators to work through the problem solving. I do not know if we have also talked about the linear independence concept yet

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6. Linear and non-homogenous general solution.

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6. Linear and non-homogenous general solution.

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7. Variation of Parameters on higher order ODE's

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What is your intuition of determinant and eigen value or your understanding of your google search?

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What is your intuition of determinant and eigen value or your understanding of your google search?

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An eigenvector is a vector that does not change when a transformation is applied to it. It becomes a scaled version of the original vector. This scalar value is known as the eigen value.

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Eigenvalues can help us determine how a system develops over time, think of Antonio's presentation as an example

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Eigen values are scalars associated with a linear system of equations, also known as characteristic roots.

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Determinant of a matrix is a special number that can be calculated from a square matrix , which has the number of rows  equal to the number of columns. Eigen values are vectors (scalar properties) 

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Determinant of a matrix is a special number that can be calculated from a square matrix , which has the number of rows  equal to the number of columns. Eigen values are vectors (scalar properties) 

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Eigenvalue is a number telling us how much variance there is in the data in that direction /or how spread out the data is on that line.

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Applying Eigen values to 2 x 2 matrix will result in the matrix tuning into [a-(lambda_1) b ; c d-(lambda_2)]. From this you able to solve for lambda_1 and lambda_2.

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The determinant is the product of eigenvalues.

det(A) =  λ1 · λ2 · · · · · λn