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

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

Solve (dy)/(dx)=(1+y)^2

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

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

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

In the parabola y^2=4ax , prove that (d^2y)/(dx^2).(d^2x)/(dy^2)=(-2a)/y^3

The second derivative of a single valued function parametrically represented by x=varphi(t)a n dy=psi(t) (where varphi(t)a n dpsi(t) are different function and varphi^(prime)(t)!=0 ) is given by (d^2y)/(dx^2)=(((dx)/(dt))((d^2y)/(dt^2))-((d^2x)/(dt^2))((dy)/(dt))/(((dx)/(dt))^2) (d^2y)/(dx^2)=(((dx)/(dt))((d^2y)/(dt^2))-((d^2x)/(dt^2))((dy)/(dt))/(((dx)/(dt))^3) (d^2y)/(dx^2)=(((d^2x)/(dt))((d^y)/(dt^2))-((d^x)/(dt^))((d^2y)/(dt^2))/(((dx)/(dt))^3) (d^2y)/(dx^2)=(((d^2x)/(dt^2))((d^y)/(dt^))-((d^2x)/(dt^2))((d^y)/(dt^))/(((dx)/(dt))^3)

Solve (dy)/(dx)=(x+2y+3)/(2x+3y+4)

Solve (dy)/(dx)=(x-2y+5)/(2x+y-1)