91Ó°ÊÓ

Find the general solution of each differential equation or state that the differential equation is not separable. If the exercise says "and check," verify that your answer is a solution. \(y^{\prime}=\frac{y}{x} \quad\) and check.

Determine the type of each differential equation: unlimited growth, limited growth, logistic growth, or none of these. \(y^{\prime}=4 y(0.04-y)\)

Use integration by parts to find each integral. $$ \int x^{5} \ln x d x $$

Evaluate each limit (or state that it does not exist). $$ \lim _{a \rightarrow-\infty} e^{-3 a} $$

Find the general solution of each differential equation or state that the differential equation is not separable. If the exercise says "and check," verify that your answer is a solution. \(y^{\prime}=\frac{y^{2}}{x^{2}} \quad\) and check

Use integration by parts to find each integral. $$ \int x^{4} \ln x d x $$

Determine the type of each differential equation: unlimited growth, limited growth, logistic growth, or none of these. \(y^{\prime}=4500(1-y)\)

Find each integral by using the integral table on the inside back cover. $$ \int \frac{1}{(2 x+1)(x+1)} d x $$

Evaluate each limit (or state that it does not exist). $$ \lim _{a \rightarrow-\infty} e^{-2 a} $$

Find the general solution of each differential equation or state that the differential equation is not separable. If the exercise says "and check," verify that your answer is a solution. \(y y^{\prime}=4 x\)