Differential Equations Answers

(1+y²)dx=(tan^-1 y-x)dy

sin^-1(dy / dx) = x + y

Find the integral surface of the PDE

(x - y) p + ( y - x - z)q = z .

A tightly stretched string with fixed end points x = 0 and x = l is initially in a position

given by y = y₀ sin³(πx/l) . It is released from rest from the initial position. Find the

displacement y(x, t) .

Solve the differential equation

xcos(y/x) (ydx+xdy) = ysin(y/x) (xdy-ydx)

Find a continuous solution of the Intial Value Problem

dy/dx + y = g(t), y(0) = 0

where g(t) = {2, when 0<=t<=1

and g(t) = {0, when t>1

Find the surface which is orthogonal to the one parameter system z = c xy( x² + y² )

which passes through the hyperbola , x² - y² = a² , z =0.

Find the general integral of the equation

(x - y) p + (y - x - z) q = z

and the particular solution through the circle z = 1, x² + y² =1

Suppose the temperature of a body when discovered is 85^o F. Two hours later, the 

temperature is 74^o F and the room temperature is 68^o F. Find the time when the body was discovered after death (assume the body temperature to be 98.6^o F at the time of death.)

Find the value of n for which the equation (n - 1)² u_xx - y²ⁿ u_yy = ny^2n-1 u_y is parabolic or hyperbolic.