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Obtain all the first and second order partial derivatives of the function: f (x, y)=x^2 sin y+y^2 cos x
((D^2)-(2DD')+(D'^2))z=(e^(x+y))+(2(x^2)y) solution
d^2x/dt^2 -6dx/dt +9x = 0, x(0) = 6, x(0) = -1
Verify the equation z(z+y^2)dx + z(z+x^2)dy - xy(x=y)=0 is intergrable and hence find its primitive
Solve the partial differential equation p cos(x+y) + q sin( x+y)=z, where the partial derivatives of z with respect to x,y are denoted by p and q respectively.
Reduce the following PDE to a set of three ODEs by the method of separation of
variables.
∂²u/∂r² + (2/r) ∂u/∂r + (1/r²) ∂²u/∂θ² + (cosθ/r²) ∂u/∂θ + (1/r² + sin²θ) ∂²u/∂φ² = 0