A curve passes through the point (-1, 1) and at any point (x, y) of the curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (-4, -3). Find the equation of the curve.

Find the equation of a curve which passes through the origin and whose differential equation is

A curve passes through the point (0, -2) and at any point (x, y) of the curve, the product of the slope of its tangent and y-coordinate of the point is equal to the x-coordinate of the point. Find the equation of the curve.

In a bank, principal increases at the rate fo r% per annum. Find the value of r if ` 100 double itself in 10 years.

(Given log_e 2 = 0.6931)

In a bank, principal increases at the rate of 5% per annum. An amount of ` 1000 is deposited in the bank. How much will it worth after 10 years?

(Given e^0.5 = 1.648)