Find the integral surface of the PDE (x - y)p + (y - x - z) q = z
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Identify the following differential equations and hence solve them
i).
ii). y = xy' + 1 - In y'.
A certain population is known to be growing at a rate given by the logistic equation
Show that the minimum rate of growth will occur when the population is equal to half the equilibrium size, that is, when the population is b/ 2a .
Suppose the temperature of a body when discovered is o 85º F. Two hours later, the temperature is o 74º F and the room temperature is o 68º F. Find the time when the body was discovered after death (assume the body temperature to be o .698º F at the time of death.)
Find the differential equations of the space curve in which the two families of surfaces u = x2 - y2 = c1 and v = y2 - z2 = c2 intersect.
Find the value of n for which the equation (n - 1)2 uxx - y2n uyy = ny2n-1 uy is parabolic or hyperbolic.
Solve the differential equation
Classify the following as true or false giving reasons for your answers..
i). For the IVP, = f(x,y), y(x0) = y0 , the continuity of f(x,y) and
guarantees the unique solution of the problem.
ii). Equations
and
have the same normal form.
iii). Equation cos(x + y) p + sin(x + y)q = z2 + z is a quasi-linear equation.
iv).
is a non -linear PDE.
v). Every solution of the ordinary differential equation (D2 + 1)2 y = 0 is bounded on [0, ∞] .