Differential Equations Answers

solve dy/dx = (y+x-2) /(y-x-4)

Solve the following Cauchy Euler equation by the method of variation of parameters.
x^2 y^n - xy'+y=2x

Determine the singular points of the following differential equation and classify each singular point as regular or irregular.

(x^2 - 9)^2 y^n + ( x+3) y' +2y = 0

Calculate Fxxyz if F(x,y,z)=sin(3x+yz) .

Solve. (X²-yz)p +(y²-zx)q =z²-xy

determine the response of the damped vibrating system given by the below mentioned differential equation using laplace transform

d2y/dt2+3dy/dt+2y=2(t^2+t+1) ;y(0)=2 ,y'(0)=0

(X^3+x)^2(x^2+x)-6=0 solve it please

Using Jacobi's method find the complete integral of the equation
2Axz + 3B y2+ B2 C =0 .

Mathematical modeling of an experiment: two competing bacterial strains,
x1 and x2, growing in a chemostat where nutrient, S, is supplied at input
concentration S0.
We know that

(a) at low nutrient concentration the rate of uptake and bacteria growth is
limited by, and proportional to, nutrient concentration,

(b) at high concentration the uptake and bacterial growth rates saturate and
become constant, independent of nutrient concentration.
This type update and growth kinetics is typically described by Michaelis-
Menten kinetics:
dx1/dt = alpha1 (x1 S /(a1 + S))

1. 1. Draw a simple diagram of the conceptual model
2. Write the differential equations for bacteria x1, x2, and nutrient S.
3. add bacteria x2 killing x1 as additional food: diagram +
equations.

find the derivative of:

2/x sqrt (9-x^2)

need step by step working out