`(dy)/(d) = x/(x^(2)+1)`

If (dy)/(dx)=4 and (d^(2)x)/(dy^(2))=-3 at a point P on the curve y=f(x) , then ((d^(2)x)/(dy^(2)))_(p)=

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 the differential equation (x^(2)+1)(dy)/(dx)+(y^(2)+1)=0 is y=2+x^(2)by=(1+x)/(1-x)c*y=x(x-1)d.y=(1-x)/(1+x)

(d^(2)x)/(dy^(2))=

(d^(2)x)/(dy^(2))=

If y=cos (mcos ^(-1) x ),then (1-x^(2)) (d^(2)y)/(dx^(2) )-x( dy)/(dx)=

If y=sin (msin ^(-1) x),then (1-x^(2))(d^(2)y)/(dx^(2))-x( dy)/(dx)=

find the order and degree of D.E : (1) ((d^(2)y)/(dx^(2) ))^2 + ((dy)/(dx))^(3) = e^(x) (2) sqrt(1 + 1/((dy)/(dx))^(2))= ((d^(2)y)/(dx^(2)))^(3/2) (3) e^((dy)/(dx))+ (dy)/(dx) =x

If y= ( tan^(-1) x)^2 , show that (1+ x^2 )( d^2 y)/(d x^2 ) + 2x(1+ x^2 ) (dy/dx) -2 = 0