Find the equation of the curve in which the subnormal varies as the square of the ordinate.

In the curve y=c e^(x/a) , the sub-tangent is constant sub-normal varies as the square of the ordinate tangent at (x_1,y_1) on the curve intersects the x-axis at a distance of (x_1-a) from the origin equation of the normal at the point where the curve cuts y-a xi s is c y+a x=c^2

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 which is such that the area of the rectangle constructed on the abscissa of any point and the intercept of the tangent at this point on the y-axis is equal to 4.

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 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 .

The differential equation of the curve for which the initial ordinate of any tangent is equal to the corresponding subnormal (a) is linear (b) is homogeneous of second degree (c) has separable variables (d) is of second order

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 line is drawn perpendicular to 5x=y+7. Find the equation of the line if the area of the triangle formed by this line with co-ordinate axes is 10 sq. units.

Find the equation of the curve passing through (2,1) which has constant sub-tangent.