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professor190 [17]
3 years ago
6

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 =
Mathematics
1 answer:
Citrus2011 [14]3 years ago
5 0

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}\\

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