Question

Find the domain for the particular solution to the differential equation dy dx equals the quotient of negative 1 times x and y, with initial condition y(2) = 2.

Answer 1

https://gyazo.com/6439d6ba1afb5baf216c9b05cf9296f0

Answer 2

@timo86m would you know?

Answer 3

sorry haven't taken DE yet

Answer 4

It's cool. I appreciate you taking your time to read the question.

Answer 5

@freckles Would you happen to know?

Answer 6

first find when when dy/dx does not exist
note dy/dx is -x/y
and -x/y is fine unless ....?

Answer 7

think fractions are not cool if the bottom is ...

Answer 8

0

Answer 9

right we don't want y to be 0...
now we need to keep this in mind after we solve the differential
equation we will try to use this

so what do you get when you solve dy/dx=-x/y

Answer 10

I got \[y = \sqrt{\frac{ -x^2 }{ 4 }+5}\]

Answer 11

not sure how you got the 5...
\[y dy=-x dx \\ \frac{y^2}{2}=\frac{-x^2}{2}+C \\ \text{ I would \not attempt \to solve for } y \text{ yet } \\ \text{ but I'm going \to use the condition given \to find } C \\ \frac{2^2}{2}=\frac{-2^2}{2}+C \\ \frac{2(2)^2}{2}=C \\ C=2^2=4 \\ \frac{y^2}{2}=\frac{-x^2}{2}+4 \\ y^2=-x^2+8 \\ \text{ but } y \neq 0 \\ \text{ so } -x^2+8 \neq 0 \text{ when ? }\]

Answer 12

What are you asking exactly?

Answer 13

for what x is -x^2+8=0?

Answer 14

\[\sqrt{8}\]

Answer 15

or?

Answer 16

-\[\sqrt{8}\]

Answer 17

-2sqrt(2) to 2sqrt(2)

Answer 18

right

Answer 19

Thanks

Answer 20

Just to confirm