In 1–8, classify the equation as separable, linear, exact, or none of these. Notice that some equations may have more than one classification.

SOLUTIONStep 1We have to check the given differential equation is separable, linear, exact.Step 2First we check given equation is linear or not.We have, a first order linear equation is of the form,Step 3Given differential equation is Which is not of the form Therefore it is not linear.Step 4Next we have to check it is separable or not.Step 5If the given differential equation is separable, then it can be written as f()d = g(y)dyStep 6.Given differential equation is This can not be expressed is of the form f()d = g(y)dy.Therefore this is not separable.Step 7Next we have to check the given differential equation is exact or not.We have, a differential equation M dx+N dy is exact if and only if Step 8Given equation is and Find = 2y= 2yHere Therefore the given differential equation is exact.Step 9We conclude that the given differential equation, is exact is not linear and is not separable.