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Differential Equations
Consider the boundary value problem(BVP) defined by laplaces equation.
uxx+uyy=0 on the square o<x,y<2
subjected to the boundary conditions:
u(0,y)=0 ,u(x,2)=0 ,u(2,y)=0 ,u(x,0)=100sin(πx/2)
Solve the BVP using method of separation of variable.
Differential Equations
Find the volume of the solid of revolution by rotating the region formed by y=3-x2 and y=2 about the line y=2
Differential Equations
Xdx+ydy=a^2.xdy-ydx/x^2+y^2
Differential Equations
Solve the following (Euler-Cauchy) differential equations:
(x^4D^4+6x^3D^3+9x^2D^2+3xD+1)y=(1+lnx)^2
(x^4D^4+6x^3D^3+9x^2D^2+3xD+1)y=(1+lnx)^2
Differential Equations
(x^4D^4+6x^3D^3+9x^2D^2+3xD+1)y=(1+lnx)^2
Differential Equations
If F(-a^2)=0, then prove that:
i.
(1/F(D^2))sinax=x(1/d/dD[F(D^2)])sinax ii. (1/F(D^2))cosax=x(1/d/dD[F(D^2)])cosax
i.
(1/F(D^2))sinax=x(1/d/dD[F(D^2)])sinax ii. (1/F(D^2))cosax=x(1/d/dD[F(D^2)])cosax
Differential Equations
z2(p2 + q2 + 1) = k2
Differential Equations
Solve (dy)/(dx)=(x-y+2)/(x-y-2)using an appropriate substitution.
Differential Equations
Find a series solution in powers of x of the equation
2x2d2y/dx2+xdy/dx+(x2-1)y=0
Differential Equations
solve
dy/dx+4xy=8x
(6xy+2y2-5)dx+(3x2+4xy-6)dy=0 y(1)=2
