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

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

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

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

(y-x(dy)/(dx))=3(1-x^(2)(dy)/(dx))

For each of the following differential equations verify that the accompanying functions a solution. Differential Function (a) x(dy)/(dx)=y, y=a x (b) x+y(dy)/(dx)=0, y=+-sqrt(a^2-x^2) (c) x(dy)/(dx)y=y^2, y=a/(x+a) (d) x^3(d^2y)/(dx^2)=1, y=a x+b+1/(2x) (e) y=((dy)/(dx))^2, y=1/4(x+-a)^2

The solution of differential equation x^(2)=1 + (x/y)^(-1) (dy)/(dx) + ((x/y)^(-2)((dy)/(dx))^(2))/(2)+.....

Find the solution of differential equation x^(2)=1 + (x/y)^(-1) (dy)/(dx) + ((x/y)^(-2)((dy)/(dx))^(2))/(2!)+.....

The solution of (dy)/(dx)=(x^2+y^2+1)/(2x y) satisfying y(1)=1 is given by

The solution of (dy)/(dx)=(x^2+y^2+1)/(2x y) satisfying y(1)=1 is given by