Problem 2E

In Problems 1–6, determine whether the given equation is separable, linear, neither, or both.

Solution:-

Step1

Given that

We have to determine whether the given equation is separable, linear, neither, nor both.

Step2

We have

The equation

Can be written as function h(x) that depends only on x times a function q(y) that depends only on y, then the equation is known as separable.

Step3

Rewrite the given equation:-

This equation , we can not write in the form of

So, by using definition of separable , this equation is not separable equation.

Step4

Linear differential equation:-

Where r(x) and s(x) are continuous functions in x.

The equation is in the form of

Where

So, is a linear equation.