Differential Equations Answers

Solve Z^3=pqxy

Solve Z(p^2+q^2)+px+qy=0

A certain population is known to be growing at a rate given by the logistic equation dx/dt=x(b-ax),where a and b are positive constants .
Show that the maximum rate of growth will occur when the population is equal to half the equilibrium size, that is, when the population is (b/2a).

Use the method of reduction of order to solve the following equation
(D^2+1)y=cosecx

Please solve the linear differential equations
1. dx/y+z = dy/-(x+z) = dz/x-y

2.(x^2D^2-3xD+5)y =x^2(logx)

q+xp=p^2

yz(y+z)dx+zx(z+x)dy+xy(x+y)dz=0

Solve the IVP:


y" + 3y' + 2y = 6((delta)base 6)(t)


with conditions: y(0) = 0, y'(0) =-1.

Find l^-1 {1/(s+1)(s+2)^2 by using convolution theorem

d^2-6dd'+9d'^2=12x^2+36xy