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

dy/dx+2xy=e^(-x^2)

Find the order and degree of the following differential equations. i) (dy)/(dx)+y=1/((dy)/(dx)) , ii) e^(e^(3)y)/(dx^(3))-x(d^(2)y)/(dx^(2))+y=0 , iii) sin^(-1)(dy)/(dx)=x+y , iv) log_(e)(dy)/(dx)=ax+by v) y(d^(2)y)/(dx^(2))+x((dy)/(dx))^(2)-4y(dy)/(dx)=0

dy/dx = e^-y (2x-4)

IF y=e^(tan^(-1)x) then prove that : (1+x^(2))(d^2y)/(dx^2)+(2x-1)(dy)/(dx)=0 .

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

The solution of the differential equation (e^x+e^(-x))dy-(e^x-e^(-x))dx =0 is

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

If y=a e^(2x)+b e^(-x) , show that, (d^2y)/(dx^2)-(dy)/(dx)-2y=0 .

dy/dx = y + e^(-2x)

If e^x+e^y=e^(x+y) , prove that (dy)/(dx)=-(e^x(e^y-1))/(e^y(e^x-1)) or, (dy)/(dx)+e^(y-x)=0