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

(dy)/(dx)=(x+y+1)/(2x+2y+3)

Solve the following differential equations. (dy)/(dx )=(1+y^2)/(1+x^2) if y=1 for x=0

(1+x^(2))(dy)/(dx)+2xy=(1)/(1+x^(2));y=0 if x=1

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

Let y=y(x) be the solution of the differential equation (dy)/(dx)=(y+1) ((y+1)e^(x^(2)/2)-x), 0 lt x lt 2.1, with y(2)=0. Then the value of (dy)/(dx) at x=1 is equal to .

(d^(2)y)/(dx^(2))=(1)/(1+x^(2)) whenx =0,y=0 and (dy)/(dx)=0

The solution of (dy)/(dx)+(2x)/(1+x^(2))y=(1)/((1+x^(2))^(2)) given that x=1,y=0 is

Solution of differential equation y-x(dy)/(dx)=y^(2)+(dy)/(dx), when x=1,y=2, is

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