Gfind the domain for the particular solution to the

Ответ:

1tallison1

13.03.2022

$\frac{dy}{dx} = \frac{-x}{y}$
by separating the variables
∴ y dy = -x dx
integrating both sides with respect to x
∴ ∫y dy = ∫-x dx
∴ $\frac{ y^{2} }{2} = - \frac{ x^{2} }{2} +c$
finding c using initial condition y(2) = 2.
∴ $\frac{ 2^{2} }{2} = - \frac{ 2^{2} }{2} +c$
∴ c = 4
∴ $\frac{ y^{2} }{2} = - \frac{ x^{2} }{2} +4$
multiplying all the equation by 2
∴ y² = -x² + 8
∴ x² + y² = 8
The resultant equation represents the equation of the circle
with center (0,0) and radius = √8 = 2√2
so, the domain of this function is [-2√2 , 2√2]
See the attached figure

Gfind the domain for the particular solution to the differential equation dy dx equals the quotient

Gfind the domain for the particular solution to the differential equation dy dx equals the quotient

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Ответ:

jakeyywashere

02.12.2021

Mathematics

Step-by-step explanation:

Idk

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Gfind 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.

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