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

(x-y)(1-(dy)/(dx))=e^(x)

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

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

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

using the subsitiution y = vx : (1) (x(dy)/(dx) -y)^(e^(y/x) =x^(2) cos x

for x>1 if (2x)^(2y)=4e^(2x-2y) then (1+log_(e)2x)^(2)(dy)/(dx)

If x^(3) dy + xy dx = x^(2) dy + 2y dx , y (2) = e and x gt 1 , then y(4) is equal to .

If (dy)/dx = (xy)/(x^2 + y^2), y(1) = 1 and y(x) = e then x =