Find the equation of the curve passing through the point and tangent at any point of which makes an angle with the x – axis.

The slope of the tangent at a point P(x, y) on a curve is If the curve passes through the point (3, – 4), find the equation of the curve.

Find the equation of the curve which passes through the point (2, 2) and satisfies the differential equation

Find the curve for which the intercept cut – off by a tangent on the x – axis is equal to four times the ordinate of the point of contact.

Show that the equation of the curve whose slope at any point is equal to y + 2x and which passes through the origin is y + 2(x + 1) = 2e^2x.