Maths

Class 12

Maths · Class 12 · Chapter 9

Differential Equations

9 lessons 65 min 2 simulations

A differential equation links an unknown function with its derivatives. Instead of giving y directly, it says how fast y changes, and the task is to recover y from that rule. This chapter defines the order and degree of such equations, separates general solutions (with arbitrary constants) from particular ones, and solves three kinds of first-order, first-degree equations: those whose variables separate, homogeneous equations, and linear equations. Growth of money, cooling of a drink and the shape of a curve with a given slope all fit these forms.

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What the exam asks

JEE Main questions on this chapter are mostly quick: the order and degree of a given equation, recognising which method fits, and solving a separable, homogeneous or linear equation with an initial condition. The linear equation with its integrating factor e^∫P dx is the most used tool. Common losses: finding the degree before clearing radicals, forgetting the constant of integration before using the initial condition, and dividing through by a term without first making the coefficient of dy/dx equal to 1.

Lessons

9 lessons · 65 min