ydy=( 1-x^2)dx/x

The integrals are 0.5y 2 = lnx-0.5x 2+c respectively.

So the general solution is 2LNX-X 2-Y 2+C = 0.

2.P(x)=- 1/x Q(x)=x^2

So the general solution is x (-∫ x 3+c) = CX-x 5/4.

3. Find the differential equation? Find a universal solution. ....

Separation variable dy/y = xdx/( 1+x 2)

Integer ln | y | = ln ((1+x 2) (1/2))+c.

Therefore, y = c (x 2+1) (1/2).

4. Normal vector of a straight line (-1/2, 1, 1)

So zx=- 1/2 zy= 1 gets x=- 1/2 y=- 1/2, and easily gets z=- 1/8.

Section equation

4x-8y-8z-3=0