Find the equation of the curve passing through the origin if the middle point of the segment of its normal from any point of the curve to the x-axis lies on the parabola `2y^2=x`

Find the equation of a curve passing through the origin, given that the slope of the tangent of the curve at any point (x,y) is equal to tha sum of the coordinates of the point.

Find the equation of the curve passing through the point (2,-3), given that the slope of the tangent to the curve at any point (x,y) is (2x)/(y^(2))

Find the equation of the curve passing through the point (0,1), if the slope of the tangent to the curve at any point (x,y), is equal to the sum of x coordinate and product of x coordinate and y coordinate of that point.

Find the equation of a curve passing through the point (0,2), given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5 .

Find the equation of a curve passing through the point (-2,3), given that the slope of the tangent to the curve at any point (x,y) is (2x)/(y^(2)) .

A curve passing through the origin has its slope. e^(x) . Find the equation of the curve.

Find the equation of a curve passing through the point (0,0) and whose differential equation is y'=e^(x)sinx.

Find the equation of a curve passing through the point (0,0) and whose differential equation is y' = e^(x) sin x .

Find the equation of the curve passing through the point (1,-1) whose differential equation is xdy=(2x^(2)-1)dx, where xne0 .

Find the equation of a straight line passing through the mid-point of a line segment joining the points (1, -5), (4, 2) and parallel to X axis