Differential Equations Answers

Solve z=px+qy-log(pq)

(x^2D^2-xD+1)y=xlogx

y'' + y' - 6y = 2x

Find the complete integral of the p.d.e P2x+Q2x= Pz using Jacobi's method

A bacterial population is known to have a logistic growth pattern with initial population 1000 and an equilibrium population of 10,000. A count shows that at the end of 1 hr there are 2000 bacteria present. Determine the population as a function of time. Determine the time at which the population is increasing most rapidly and draw a sketch of the logistic curve.

ysin2xdx=(1+y^2+cos^2x)dy

4xyz=pq+2px^2y+2qxy^2

z=px+qy+3(pq)^1/3

yp+x^2q^2=2x^2y

Determine the steady-state temperature u(x,y) in a rectangular plate A(0,0), B(0,6), C(10,6), D(10,0) if the temperature along AB, BC, and AD are maintained at zero while edge CD is at temperature 80. Note that the flat faces are insulated.