Differential Equations Answers

The rate of increase of the population of bateria in a culture is proportional to the number of bacteria at any given instant. Assume the initial count of bacteria is 1000 and after 1 hour the amount is 1200. Find (i) the number of bacteria present immediately after 5 hours. (iii) the time lapse before the number reaches 4000

Find the general solution of the DE(y^2-2xy+6x)dx-(x^2-2xy+2)dy=0

Find the general solution of the DE 3y( x2 - 1) dx  (x3  8y – 3x) dy = 0

E xplain the general m otion of a Sim ple P endulum .

(D^4 − 18D^3 + 119D^2 − 342D + 360)y = 0

1/x+ye^xy+2x)dx +(1/y+xe^xy+2y)dy=0

ACTIVITY IN BASIC CALCULUS

QUOTIENT RULE

  I. Find the derivative of the following functions below using the quotient rule. Show your complete solution.

1. "\\frac{x^2-7x}{2x^3+5x^2}"
2. "\\frac{3x^2+7x-14}{x^3-4x^2}"
3. "\\frac{2x^3+8x^2}{x^2+6x^2-10}"

II. Create your own given problem involving quotient rule and solve. Show your complete solution. Do not copy the given example below.

1. Example must have two different terms in numerator, and three different terms in denominator

eg. (do not copy)

y= "\\frac{8x^2-3x}{x^2+6x^2-10}"

2. Example must have three different terms in numerator, and three different terms in denominator

eg. (do not copy)

y= "\\frac{x^2+8x^2-3x}{2x^3+6x^2-10}"

(dy)/(dx) = - x/(2y)

Find canonical form of Zxx +Zyy=y

Find the general solution of the following differential equation using the method of

undetermined coefficients: d^y/dx^2 - dy/dx + 2y = 2cosh2x