Consider the following differential equation. x^2y' + xy = 3 (a) Show that every member of the family of functions y = (3ln(x) + C)/x is a solution of the differential equation. (Do this on paper. Your instructor may ask you to turn in this work.) (b) Illustrate part (a) by graphing several members of the family of solutions on a common screen. (Do this on paper. Your instructor may ask you to turn in this work.) (c) Find a solution of the differential equation that satisfies the initial condition y(1) = 8. (Enter the argument of the logarithmic function in parentheses.) y(x) = (d) Find a solution of the differential equation that satisfies the initial condition y(8) = 1. (Enter the argument of the logarithmic function in parentheses.) y(x) =

Plz i want answer and i would appreciate it is is a b c or d

What is the equation and solution for the sentence? the sum of a number and thirty-one is one hundred thirteen. write the equation as n-31=113 and subtract 31 from both sides. the answer is 82. write the equation as n+31=113 and subtract 31 from both sides. the answer is 82. write the equation as n+31=113 and add 31 to both sides. the answer is 144. write the equation as n-31=113 and add 31 to both sides. the answer is 144.

Browning labs is testing a new growth inhibitor for a certain type of bacteria. the bacteria naturally grows exponentially each hour at a rate of 6.2%. the researchers know that the inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. the sample currently contains 100 bacteria.the container holding the sample can hold only 300 bacteria, after which the sample will no longer grow. however, the researchers are increasing the size of the container at a constant rate allowing the container to hold 100 more bacteria each hour. they would like to determine the possible number of bacteria in the container over time.create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.