Differential Equations Answers

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

dy/dx+ycotx=5e^cosx

(D²+2DD'+D'²)z=x³

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.

(1+yx)x dy+(1-yx)y dx=0

Solve the initial value problem :

d²x/dt² -6dx/dt + 9x = 0 , x(0) =6 ,x(0) = -1 .

1. a) Solve the following ordinary differential equations:

i) dy/dx + 4xy = x

ii) d²y/dx² + 4dy/dx - 12y = cos2x .

the normal form of the differential equation y"-xy'+(4x^2-1)y=?