Solve `(d^2y)/(dx^2)=((dy)/(dx))^2`

Solve: (d^2y)/dx^2=x

Show that A x^2+B y^2=1 is a solution of the differential equation x{y\ (d^2y)/(dx^2)+((dy)/(dx))^2}=y(dy)/(dx)dot

Show that A x^2+B y^2=1 is a solution of the differential equation x{y\ (d^2y)/(dx^2)+((dy)/(dx))^2}=y(dy)/(dx)dot

for any differential function y= F (x) : the value of ( d^2 y) /( dx^2) +((dy)/(dx)) ^3 . (d^2 x)/( dy^2)

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

Solve: (dy)/(dx)=(2y)/x

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

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

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

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