Examples of using Y squared in English and their translations into German
{-}
-
Colloquial
-
Official
-
Ecclesiastic
-
Medicine
-
Financial
-
Ecclesiastic
-
Political
-
Computer
-
Programming
-
Official/political
-
Political
It's y squared minus 2y.
First of all, you have a y squared.
And then y squared is just a constant, right?
Maybe it's just, I don't know, y squared i.
So to have the y squared, that makes it non-linear.
And then y times y, well that's just y squared.
So let me add x over y squared dy dx to both sides.
The only difference between that and that is they put y's here.Y and a y squared.
So it's 2 y squared. Minus 0 squared over 2 times y squared.
And this one is-- this one looks simpler. x minus y squared is equal to 8 timesy minus 6.
Well, it's y squared, is equal to-- I will do the plus c on this side.
This square root of y squared, this is just y. .
So the first separable differential equation is:dy over dx is equal to x squared over 1 minus y squared.
So you get 1 minus y squared dy is equal to x squared dx.
Over y plus, or maybe I should say minus, minus-- if I just simplify this,this is x over y squared times dy dx.
So this is equal to dy dx times x over y squared plus cosine squared of x over y. .
So you get y squared is equal to r squared minus x squared. y is equal to the square root of r squared minus x squared. .
The natural log of the absolute value of y plus y squared is equal to sine of x plus 1.
If X squared plus Y squared equals 16.-- How do we find DYIDX as an implicit function of X and Y? .
So this is the same thingas 8 to the third power times x to the third power times y squared to the third power.
The integral of 1 is y, the integral of y squared, well that's minus y to the third over 3.
So the radius away from the center, that's just going to be rsquared is just x squared plus y squared plus z squared. .
They're giving us y squared minus x, whole thing squared. x is equal to 2 and y is equal to 1.
So if I'm justmultiplying both sides of this equation times 1 minus y squared, you get 1 minus y squared times dy dx is equal to x squared. .
So that is x over y squared-- I will write the dy dx in orange. dy dx, and then you have this term, plus cosine squared of x over y dy dx.
And even if this was a y, if you were to actually multiply both sides of this equation times 1 minus y, and get in the form that I showed you in the previous equation,you would have 1 minus y squared.
And then if you divide minus 6y squared by 3y,minus six divided by 3 is minus 2, y squared divided by y is y. .
So this is equal to 512 times x to the third and y squared to the third power, that's the same thing is y to the 2 times 3 power, or y to the sixth power.
And the left hand side will be 1 over y minus x over y squared dy dx is equal to-- I have to multiply both side of the equation times this denominator right here-- is equal to cosine squared of x over y plus cosine squared of x over y dy dx.