Find the general solution of the differential equation ydx−(x+2y2)dy=0.
A curve y=f(x) passes through point P(1,1) . The normal to the curve at P is a (y−1)+(x−1)=0 . If the slope of the tangent at any point on the curve is proportional to the ordinate of the point, then the equation of the curve is
The curve passing through the point (1,1) satisfies the differential equation dxdy+xy(x2−1)(y2−1)=0 . If the curve passes through the point (2,k), then the value of [k] is (where [.] represents greatest integer function)_____
Determine the equation of the curve passing through the origin, in the form y=f(x), which satisfies the differential equation dxdy=sin(10x+6y)˙