ordinary differential equations - Solution of $ (x^2 + y^2)\ dx -2xy ...
Jun 29, 2015 · When I forgot the minus in the second term ($-2xy$) I got the same wrong solution you got with Bernoulli, so you should just check your method again and be careful with the signs. Share Cite
Deriving the Formula for Average Speed (Same distance).
Let me start of by specifying the question: A and B are two towns. Kim covers the distance from A to B on a scooter at 17Km/hr and returns to A on a bicycle at 8km/hr.What is his average sp...
How do I prove $2xy ≤ x^2+y^2$? - Mathematics Stack Exchange
Oct 7, 2018 · I'm quite new at calculus, how could I prove: $$2xy ≤ x^2 + y^2$$ I just can end up in $(xy)^{1/2} ≤ (x+y)/2$. And even though I know that this is true too, I don't know how to prove it either. T...
ordinary differential equations - How to solve $y' + xy^2 = 2xy ...
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How do I prove that $x^2 + y^2 = (x + y) ^2 – 2xy$ geometrically ...
May 9, 2015 · The answers offered so far just introduce $-2xy$ without explaining where it comes from (except as the inverse of $+2xy$). Remark: I am perfectly aware that $$(a + b)^2= a^2 + 2ab + b^2$$ and that one can subtract $2ab$ and it works.
How to prove $2x^2 + 2y^2 + 2z^2 -2xy -2yz \\geq 0$
Dec 13, 2019 · I know how to prove $2x^2 + 2y^2 + 2z^2 -2xy -2yz -2xz \geq 0$ since I can split it up in the three terms $(x-y)^2, (y-z)^2, (z-x)^2$ which are all greater than or equal to zero, but how do I prove...
solving the differential equation $y'=2xy$, $y(0)=2$
Whenever you solve a separable ODE, you should begin by identifying any stationary solutions to the equation. Provided you have uniqueness, any other solutions will never cross the stationary solutions, so that all solutions are either completely stationary or can be found by separation of …
ordinary differential equations - Power series solution to $y’ + 2xy ...
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real analysis - Solving $y'' - 2xy' - 2y = 0$ using power series ...
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quadratic forms - show that the function $z = 2x^2 + y^2 +2xy
Now the polynomial becomes $$ 2X^2+2XY+Y^2-3 $$ and now it is clear that its values are $\ge-3$, because $2X^2+2XY+Y^2$ is positive definite (the conic is an ellipse), having negative discriminant $4-8=-4$. Or you can write it as $$ X^2+(X+Y)^2-3 $$