`(dy)/(dx)=(d(1/(1+x)))/(dx)`

STATEMENT -1 : for the function y= f(x), f(x) ,({1+((dy)/dx)^(2)}^(3/2))/((d^(2)y)/(dx^(2))) = - ({1+ (dx/dy)^(2)}^(3/2))/((d^(2)x)/(dy^(2))) STATEMENT -2 : (dy)/(dx) = (1/(dx))/dy and (d^(2)y)/(dx^(2)) = d/dx (dy/(dx))

The degree of the differential equation x=1+((dy)/(dx))+1/(2!)((dy)/(dx))^2+1/(3!)((dy)/(dx))^3+............. (A) 3 (B) 2 (C) 1 (D) not defined

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

If y=xlog(x/(a+b x)),t h e nx^3(d^2y)/(dx^2)= (a) x(dy)/(dx)-y (b) (x(dy)/(dx)-y)^2 y(dy)/(dx)-x (d) (y(dy)/(dx)-x)^2

Solve the initial value problem: y-x(dy)/(dx)=2(1+x^2(dy)/(dx)),\ y(1)=1

(d^2x)/(dy^2) equals: (1) ((d^2y)/(dx^2))^(-1) (2) -((d^2y)/(dx^2))^(-1)((dy)/(dx))^(-3) (3) ((d^2y)/(dx^2))^(-1)((dy)/(dx))^(-2) (4) -((d^2y)/(dx^2))^(-1)((dy)/(dx))^(-3)

If e^y(x+1)=1, show that (d^(2y))/(dx^2)=((dy)/(dx))^2 If y=sin(2sin^(-1)x), show that ((1-x^2)d^(2y))/(dx^2)=x(dy)/(dx)-4y

If e^y(x+1)=1 , show that (d^2y)/(dx^2)=((dy)/(dx))^2 .

If e^y(x+1)=1 . Show that (d^2y)/(dx^2)=((dy)/(dx))^2

If e^y(x+1)=1 , show that (d^2y)/(dx^2)=((dy)/(dx))^2 .