Determine whether each first-order differential equation is separable, linear, both, or neither. 1. +=x2y2 2. y+sinx=x3y′ 3. lnx−x2y=xy′ 4. +cosy=tanx

a) Linear

b) Linear

c) Linear

d) Neither

See explanation below.

Step-by-step explanation:

a)

For this case the differential equation have the following general form:

Where and and since n>1 we can see that is a linear differential equation.

b)

We can rewrite the following equation on this way:

For this case the differential equation have the following general form:

Where and and since n=0 we can see that is a linear differential equation.

c)

For this case we can write the differential equation on this way:

For this case the differential equation have the following general form:

Where and and since n=0 we can see that is a linear differential equation.

d)

For this case we can't express the differential equation in terms:

So the is not linear, and since we can separate the variables in order to integrate is not separable. So then the answer for this one is neither.

step-by-step explanation: it is d

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