Differential Equations Answers

Find the complete integral of the equation
∂z/∂x[1+(∂z/∂y) ^2]=∂z/∂y(z-a)

d2^x/dt^2 - 6 dx/dt +9x =0; when t =0, x =2 and dx/dt = 0

Find the general equation of surfaces orthogonal to the family given by
(a) x(x^2+y^2+z^2)=c1y^2
Showing that one such orthogonal set consists of the family of spheres given by
(b) x^2+y^2-z^2=c2z
If a family exists, orthogonal to both (a) and (b) show that it must satisfy
2x(x^2-z^2)dx+y(3x^2+y^2-z^2)dy+2z(2x^2+y^2)dz=0
Show that such a family in fact exists and find its equation.

Solve
x(x^2+y^2-a^2)dx+y(x^2+y^2-b^2)dy=0

Find the equation of integral surface to the differential equation
2y(z-3)p+(2x-z)q=y(2x-3)

Find the equation of integral surface to the differential equation
2y(z-3)p+(2x-z)q=y(2x-3)

Solve dy/dx +2xy= 1+x²+y² given y'(x)=x is a solution.

e^x dx+(e^x coty +2ycscy)dy=0

y'+2ty=4t^3

Solve:(p − q)z = z^2 + (x + y)^2