Chapter 3: Differential EquationsClass 12 Mathematics — summary, notes, extra questions & MCQ quiz

Summary

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 \(\dfrac{dy}{dx}=g(x)h(y)\) is rearranged and integrated; homogeneous equations, solved by the substitution \(y=vx\); and linear equations \(\dfrac{dy}{dx}+Py=Q\), solved using the integrating factor \(e^{\int P\,dx}\). Differential equations model growth, decay and many physical processes.

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