" (NCERT) "12.(1-x)dy-(1+y)dx=0.

y(1+x)dx+x(1+y)dy=0

y(1+x)dx+x(1+y)dy=0

(1)/(x)dy-(1)/(y^(3))dx=0

Solve y(1+x)dx+x(1+y)dy=0

(1+x)(1-y)(dy)/(dx)+xy=0

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

Express (1+e^(x//y)) dx+e^(x//y) (1-(x)/(y)) dy=0 in the form (dx)/(dy) = F((x)/(y)) .

For each of the following initial value problems verify that the accompanying functions is a solution. (i) x(dy)/(dx)=1, y(1)=0 => y=logx (ii) (dy)/(dx)=y , y(0)=1 => y=e^x (iii) (d^2y)/(dx^2)+y=0, y(0)=0, y^(prime)(0)=1 => y=sinx (iv) (d^2y)/(dx^2)-(dy)/(dx)=0, y(0)=2, y^(prime)(0)=1 => y=e^x+1 (v) (dy)/(dx)+y=2, y(0)=3 => y=e^(-x)+2