Differential Equations Answers

If d2x/dt2+g(x-a)/b=0, (a, b, gbeing positive constants) and x = a′ and dx/dt=0 when t=0, show that x=a+(a'-a)cos {g underoot t/b}

Solve the partial differential equation

(D+D'-1)(D+2D'-3)z=4+3x+6y

Find the surface which is orthogonal to the one parameter system
z=c xy(x^2+y^2) and which passes through the hyperbola
X^2-y^2=a,z=0.

Find the general integral of the equation
(Xyy)p+(y-x-z)q=z
and particular solution through the circle
Z=1,x^2+y^2=1.

1.Find the differential equations of the space curve in which the two families of surfaces u=x^2-y^2=c1 andv=y^2-z^2=c2 intersect.
2. Find value of n for which the equation (n-1)^2 u_xx-y^2n u_yy=ny^(2n-1) u_y is parabolic or hyperbolic.

Solve the differential equation
Suppose the temperature of a body when discovered is 85° F. Two hours later, the temperature is 74°F and the room temperature is 68°F. Find the time when the body was discovered after death (assume the body temperature to be 98.6°F at the time of death.)

Solve the differential equation
1.sin^-1(dy/dx)=(x+y)
2.(1+y^2)dx=(tan^-1y-x)dy
3.(D-1)^2(D^2+1)^2y=sin^2(x/2)+e^x+x
4.2x^2y(d^2y/dx^2)+4y^2=x^2(dy/dx)^2+2xy(dy/dx)

Obtain a solution of the wave equation
∂^2u(x,t)/∂t^2=16(∂^2u(x,t)/∂x^2)

for 0≤ x ≤ π and t > ,0 and the following boundary and initial conditions:
u(0,t)=u(π,t)=0,
u(x,0)=x(π-x) and ∂u(x,0)/∂t=0

Obtain the Fourier series expansion for the following periodic function which has a
period of π: f(x)={(4/π) for 0<x<π/2

obtain all the first and second order PD of the fuction f(x,y)=(x^2)Siny+(y^2)cosx