Differential Equations Answers

Using Taylor series expression, find a power series solution for the equation

2x²d²y/dx²-xdy/dx+(x-5)y=0 in powers of (x-1) if y(1)=4 and y'(1)=2

The population P, t years after the initial observation is given by the formula:

p_t=(100000)/(2+3e^-0.05t)

Determine the exact size of the population and the time in years when the rate of growth is maximum

Find the relation of the variable w if the growth rate is given by

dw/dt=(kw(α-w))/α, k>0, at t=0,w=α/(1+β)

Using annihilator method obtain particular solution of y"'+y= cosx+sinx

Determine the Green, s function and express the solution as a definite integral

-y^''=f(x), y(0)=0, y'(1)=0

Determine the Green function and express the solution as a definite integral

-(y^''+y)=f(x), y^'(0)=0, y(1)=0

A tank having a capacity of 1000 liters, initially contains 400 liters of sugar water having a concen-

tration of 0.2 Kg of sugar for each liter of water. At time zero, sugar water with a concentration of

50 gm of sugar per liter begins pumped into the tank at a rate of 2 liter per minute. Simultaneously,

a drain is opened at the bottom of the tank so that the volume of the sugar-water solution in the

tank reduces 1 liter per minute. Determine the following: