Find the characteristics values and the characteristics functions of the sturn_liouville problem
d/dx[x(dy/dx]+(λ /x)y=0,
y1(1)=0, y1(e(2π))=0 where λ>0
Use the laplace transform to solve the one dimensional boundary value problem
∂u/∂t=∂2u/∂x2, 0<x<1, t>0
subject to u(x,0)=sin πx, u(0,t)=0, u(1,t)=0
Find the integral surface of the equation x2p+y2q+z2=0 passing through z=1,x+y=xy
Determine the laplace transform of
i) ∂u(x,t)/∂t
ii)∂2u(x,t)/∂x2
By the method of separation of variables, solve the boundary value problem
∂u/∂x=4∂u/∂y, u(0,y)=8e-3y
Find the non-trivial solution of the sturn_liouville problem d2y/dx2+λy=0 y(0)=0, y(π)=0
Define a partial differential equation and give an example.
Hence find the differential equation arising from F[y/x,z/x3]=0
Using the Laplace transform method, solve the partial differential equation
∂u/∂t=u-∂u/∂x. Subject to the initial condition u(x,0)=e-7x, x>0,t>0
Find the integral surface of the equation 4yzp+q+2y=0 passing through
y2+z2=2,x+z=1
Find the integral surface of the equation 4yzp+q+2y=0 passing through
y2+z2=2,x+z=1