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3 years ago

X+2y=3 x-y=6 x=? y=?

2 answers:

3 0

Set each equation equal to either x or y.

I’ll do x.

x+2y-2y = 3-2y
(Simplify) x = 3-2y

x-y+y = 6+y
(Simplify) x = 6+y

(Set them equal to each other)
3-2y = 6+y

3-2y-6 = 6+y+2y

-3 = 3y

y = -1
x =5

spin [16.1K]3 years ago

3 0

Answer:

x=5

y=-1

Step-by-step explanation:

x+2y=3

x-y=6

x+2y=3

x=6+y

(6+y)+2y=3

x=6+y

6+y+2y=3

x=6+y

6+3y=3

x=6+y

3y=3-6

x=6+y

3y=-3

x=6+y

y=-3/3

x=6+y

y=-1

x=6-1

y=-1

x=5

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3 years ago

Consider the differential equation: xy′(x2+7)y=cos(x)+e3xy. Put the differential equation into the form: y′+p(x)y=g(x), determin

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Answer:

Linear and non-homogeneous.

Step-by-step explanation:

We are given that

$\frac{xy'}{(x^2+7)y}=cosx+\frac{e^{3x}}{y}$

We have to convert into y'+P(x)y=g(x) and determine P(x) and g(x).

We have also find type of differential equation.

$y'=\frac{(x^2+7)y}{x}(cosx+\frac{e^{3x}}{y}}$

$y'=\frac{(x^2+7)cosx}{x}y+\frac{(x^2+7)e^{3x}}{x}$

$y'-\frac{cosx(x^2+7)}{x}y=\frac{e^{3x}(x^2+7)}{x}$

It is linear differential equation because this equation is of the form

y'+P(x)y=g(x)

Compare it with first order first degree linear differential equation

$y'+P(x)y=g(x)$

$P(x)=-\frac{cosx (x^2+7)}{x},g(x)=\frac{e^{3x}(x^2+7)}{x}$

$\frac{dy}{dx}=\frac{(x^2+7)(ycosx+e^{3x})}{x}$

Homogeneous equation

$\frac{dy}{dx}=\frac{f(x,y)}{g(x,y)}$

Degree of f and g are same.

$f(x,y)=(x^2+7)(ycosx+e^{3x}),g(x,y)=x$

Degree of f and g are not same .

Therefore, it is non- homogeneous .

Linear and non-homogeneous.

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3 years ago

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Answer:

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Step-by-step explanation:

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