The differential equation of all the ellipses centred at the origin and have axes as the co-ordinate axes is
where `y'=(dy)/(dx), y''=(d^(2)y)/(dx^(2))`

Find (dy)/(dx) , when y=(ax^(2)+b)^((9)/(2))

differentiate y=cos x+sin2x

Solve the differential equation (x)dy = ( 1 + y^(2))dx .

Show that , the equation of all circles touching the y-axis at the origin is , 2xy (dy)/(dx) = y^(2) - x^(2)

An ellipse is drawn by taking a diameter of the circle (x-1)^(2) + y^(2) = 1 as its semi-minor axis and a diameter of the the circle x^(2) +(y - 2)^(2) = 4 as its sem-major axis . If the centre of the ellipse is at the origin and its axes are the coordinate axes , then the equation of the ellipse is _

The solution of the differential equation y-x(dy)/(dx)=a(y^(2)+(dy)/(dx)) is -

If y=e^(ax)cos bx , Then find [(d^(2)y)/(dx^(2))]_(x=0)

The degree of the differential equation [1+((dy)/(dx))^(2)]^(5//3)=(d^(2)y)/(dx^(2)) is

Solve the differential equation y dx = (x + y^(2))dy ( y ne 0) .