Classify the equation according to its type Select ALL that

Classify the equation according to its type. Select ALL that apply. (x+1)dy/dx + y = y^3 In (x) Select one or more: a. 1st order b. Bernoulli c. 2nd order d. Separable e. linear An object is taken out of the freezer (0 degree C) and placed on a table in a 20 degree C room. Ten minutes later the temperature is 2 degree C. It warms according to Newton\'s Law. How long does it take before the temperature reaches 15 degree C? Select one: a. 127 minutes b. 122 minutes c. 132 minutes d. 142 minutes e. 137 minutes

Solution

Given that

(x + 1)dy/dx + y = y³ln(x)

Dividing on both sides by (x+1)

dy/dx + (1/(x+1))y = y³ln(x) / (x+1)

dy/dx + (1/(x+1))y = [ln(x) / (x+1)]y³

If the equation is in the form of dy/dx + p(x)y = q(x)yⁿ then that equation is called as first order Bernoulli equation