Differential Equations Answers

Find the integral surface of the linear partial differential equation x(x^2+z)p - y(y^2+z)q = (x^2-y^2)z; p, q has their usual meaning , which contains the straight line. [CO1] *

Given x and y are species whose interaction is governed by x¹=x(-20-x+2y) and y¹=y(-50+x-y) ..... identify the type of interaction 2) determine equilibrium point of model and state possible outcomes of this interaction 3)linearise the system around each equilibrium point and discuss the nature of stability of each equilibrium point....4)sketch phase portrait of the above system

The population of a certain state is known to grow at a rate proportional to the number of people presently living in the state. If after 10 years the population has trebled and if after 20 years the population is 150,000, find the number of people initially living in the state

Under certain conditions, cane sugar is converted into dextrose at a rate, which is proportional to the amount unconverted at any time. If out of 60 grams of sugar at t = 0 6 grams are converted during the first 4 minutes, find the amount converted in 2 hours.

1. Solve the following Bernoulli's Differential Equations. Show your solutions.

a. dy/dx + (1/3) y = e^x y²

b. x (dy/dx) + y = xy³

c. dy/dx + (2/x) y = -x² cos x y²

d. x²y-x³ (dy/dx) = y² cos x

(2xy+3y2)dx-(2xy+X2)dy=0

A condenser of capacity C=5*10^5 farad is charged through a resistance R=200ohms by steady voltage E=2000volts.Calculate the current at the instant of closing the switch