" 1."(1+x^(2))dx+(1+y^(2))dy=0

y(1+x^(2))dy=x(1+y^(2))dx

y(1-x^(2))dy=x(1+y^(2))dx

x(2y-1)dx+(x^(2)+1)dy=0

Solve the following differential equations. (i) (dy)/(dx) =(1+y^(2))/(1+x^(2)) (ii) (dy)/(dx) = (sqrt(1-y^(2)))/(sqrt(1-x^(2))) (iii) (dy)/(dx) = 2y tan hx (iv) sqrt(1+x^(2))dx + sqrt(1+y^(2))dy = 0 (v) (dy)/(dy) = e^(x-y)+x^(2)e^(-y)

Solve the differential equation (1+x)(1+y^(2))dx+(1+y)(1+x^(2))dy =0.

x(1+y^(2))dx+y(1+x^(2))dy=0 at (0, 0)

If y = (1 + x) (1 + x^(2)) .. (1 + x^(2n)) , then ((dy)/(dx))_(x = 0) is equal to

If y=sin^(-1)x then prove that (1-x^(2))(d^(y))/(dx^(2))-x(dy)/(dx)=0

The solution of the differential equation (1+y^(2)) tan^(-1) x dx + y(1+x^(2)) dy = 0 is