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A tightly stretched string with fixed end points x=0 and x=l is initially in a position given by y=y0sin^3(πx/l).It is released from rest from the initial position. Find the displacement y(x,t).
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.
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.
(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.
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.
Verified that the equations
1.z=root(
2x+a)+root(2y+b) and
2.z^2+meu=2(1+lemda^-1)(x+lemda y)
are both complete integrals of the PDE z=1/p+1/q.Also show that the complete integral (2)is the envelope of the one parameter sub-system obtained by taking b=-a/lemda-meu/(1+lemda) in the solution (1)
1.z=root(
2x+a)+root(2y+b) and
2.z^2+meu=2(1+lemda^-1)(x+lemda y)
are both complete integrals of the PDE z=1/p+1/q.Also show that the complete integral (2)is the envelope of the one parameter sub-system obtained by taking b=-a/lemda-meu/(1+lemda) in the solution (1)
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.)
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)
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)
kristen replays 425$ per month over 5 years on her car loan of 20,000. what flat rate of interest was kristen being charge
50 apples cost $25. How much would 75 apples cost?
Math
Reduce the following PDE to a set of three ODEs by the method of separation of
variables (1/r)(∂/∂r)(r(∂V/∂r)+(1/r^2)(∂^2V/∂θ^2)+(∂^2V/∂z^2)+(k^2)V=0
variables (1/r)(∂/∂r)(r(∂V/∂r)+(1/r^2)(∂^2V/∂θ^2)+(∂^2V/∂z^2)+(k^2)V=0
