Question

Consider the differential equation dy/dx = 4 − y. (a) Either by inspection or by the concept that y = c, −[infinity] < x < [infinity], is a constant function if and only if y' = 0, find a constant solution of the DE. y =

Answer 1

Answer:

$y=4-e^{-x-C}$

Step-by-step explanation:

Differential equation is an equation consisting of variables and derivatives.

A variable is a term whose value varies.

Integration is used to find area under the curve and to find the volume.

In $\int f(x)\,dx$, x is a variable of integration and f(x) is the integrand.

Given:

$\frac{\mathrm{d} y}{\mathrm{d} x}=4-y$

Formulae Used:

$\int \frac{dy}{y}=\ln y\\\int dx=x\\\ln a=b\Rightarrow a=e^b$

Integrate both sides.

$\int \frac{dy}{4-y}=\int dx\\-\ln (4-y)=x+C\\4-y=e^{-x-C}\\y=4-e^{-x-C}$

Answer 2

The solution of differential equation is , $ln(\frac{1}{y-4} )=x+c$

Given differential equation is,

                $\frac{dy}{dx}=4-y\\\\-\frac{1}{y-4}dy =dx$

Integrate both side.

     $-ln(y-4)=x+c\\\\ln(\frac{1}{y-4} )=x+c$

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