Solve the following homogeneous equations by using an appropriate substitution.
1. Xy’ = y^ 2/x + y.
2. xdx + (y-2x) dy = 0
3. (x+y) dx +xdy = 0
4. Xy^2 dt/dx = y^3 – x^3 y(1)=2
Solve the given Bernoulli differential equations by using an appropriate substitution.
5. dx/dx - y=e^xy^²
6. y' -2/xy=x^6y^²
7. x dy/dx+y= 1/y^2
8. X^2 –dy/dx - 2xy = 3y^4