(1+x²+y²+x²y²) ^1/2 + xy dy/dx =0 how to solve dis diffrential equation!?! ..please ans asap!! :)

1. Solve diff eqn   dy/dx  +  y cotx  =  x2 cotx  +  2x
2. Find distance of the point (-2 , 3 , -4 )  from the line  x + 2/3 = 2y +3/4 = 3z + 4/5  m,easutres II to plane   4x + 12y - 3z +1 =0

how can we solve ; dy/dx=tan 2(x+y) or dy/dx=tan square (x+y)

number chart for maths fair

Solve (1+y²)dx = (tan^-1y - x)dy

if x=a(t+sint) , y=a(1-cost) , show that y''=1/a , at t=90deegre .(or) pi/2

dy/dx+xsin2y=x³cos²y

Solve the differential equation:

x dy/dx + y = x cosx + sinx

given that y(pie/2) =1.

form the differential equation of a family of circles touching y- axis at origin

Solve:

dy/dx = 1 + x + y + xy

Answer given in the book is : log | 1 + y| = x + 1/2 x² + C