Question

Solve the given differential equation by separation of variables dn/dt n = nte^t 8

Answer 1

The answer of the given question will be - $ln |n| + c = e^{8+t} t - e^{8+t} - t + c$

What is integration?

In mathematics, integration is a technique for combining or adding the parts to arrive at the total. It is a form of differentiation in reverse where we break down functions into their component elements. This technique is employed to determine the summation on a sizable scale.

We are given the equation as -

$\int\limits^_ {}$dn/dt + n = $\int\limits^_ {}$$nte^{t+8}$

⇒ dn/dt = $nte^{t+8} - n$

$dn/dt = n(te^{t+8} - 1)\\dn/n = (te^{t+8} - 1)dt$

Integrating on both sides,

⇒ ln |n| + c =$\int\limits^$$nte^{t+8} - n$

⇒ ln |n| + c = $e^{8+t} t - e^{8+t} - t + c$

To learn more about integration from given link

brainly.com/question/27419605

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