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

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

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

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

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

If x=log pandy=(1)/(p), then (a) (d^(2)y)/(dx^(2))-2p=0 (b) (d^(2)y)/(dx^(2))+y=0 (c) (d^(2)y)/(dx^(2))+(dy)/(dx)=0( d) (d^(2)y)/(dx^(2))-(dy)/(dx)=0

(a+bx)e^((y)/(x))=x, Prove that x^(3)(d^(2)y)/(dx^(2))=(x(dy)/(dx)-y)^(2)

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

The first integral of (dy)/(dx)((d^(2)y)/(dx^(2)))-x^(2)y((dy)/(dx))=xy^(2) will be

If y=x log((x)/(a+bx)), thenx ^(3)(d^(2)y)/(dx^(2))= (a) x(dy)/(dx)-y (b) (x(dy)/(dx)-y)^(2)y(dy)/(dx)-x(d)(y(dy)/(dx)-x)^(2)

Find degree and order x(d^(2)y)/(dx^(2))+((dy)/(dx))^(5)-y(dy)/(dx)=3