ordinary differential equations - How to solve $y' + xy^2 = 2xy ...
2016年11月4日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
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 …
How to prove $2x^2 + 2y^2 + 2z^2 -2xy -2yz \geq 0$
2019年12月13日 · 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...
ordinary differential equations - Solution of $ (x^2 + y^2)\ dx -2xy ...
2015年6月29日 · $\frac{dy}{dx}=\frac{x^2+y^2}{2xy} $..(i) This is a homogeneous differential equation because it has homogeneous functions of same degree 2. homogeneous functions are: $(x^2+y^2)$ and $2xy$, both functions have degree 2. Solution of differential equation: Equation (i) can be written as, $\frac{dy}{dx}=\frac{1+\frac{y}{x}}{2(\frac{y}{x})}$..(ii)
How do I prove $2xy ≤ x^2+y^2$? - Mathematics Stack Exchange
2018年10月7日 · $$2xy ≤ x^2 + y^2$$ I just can end up in $(xy)^{1/2} ≤ (x+y)/2$. And even though I know that this is ...
Find the value of $2xy$ - Mathematics Stack Exchange
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Solution of the differential equation $y'' + 2xy' + \left( 1 + x^2 ...
2017年10月29日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
How to factor$ x^2+2xy+y^2 - Mathematics Stack Exchange
2015年9月16日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
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 $$ X^2+(X+Y)^2-3 $$
How do I prove that $x^2 + y^2 = (x + y) ^2 – 2xy$ geometrically ...
2015年5月9日 · 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.