Differential Equations — Class 12 Mathematics

A differential equation relates a function to its derivatives. Its order is the order of the highest derivative present, and its degree (when defined) is the power of that highest-order derivative once the equation is a polynomial in derivatives. A solution containing as many arbitrary constants as the order is the general solution; fixing the constants from initial conditions gives a particular solution. This chapter covers the formation of differential equations and three methods of solving first-order, first-degree equations: variables separable, where is rearranged and integrated; homogeneous equations, solved by the substitution ; and linear equations , solved using the integrating factor . Differential equations model growth, decay and many physical processes.