Differential Equations

Board: GSEB Class: 12

Chapter Overview

A differential equation contains derivatives of a function. Order = highest derivative. Degree = power of highest derivative (after clearing radicals). Solution types: general (with constants) and particular (given initial conditions). Methods: variable separable, homogeneous equations (y = vx substitution), linear DEs (integrating factor method), and Bernoulli equations.

Topics Covered

Order and Degree
Formation of DE
Variable Separable
Homogeneous Equations
Linear Differential Equations
Bernoulli Equations
Initial Value Problems

Key Formulas

General solution: y = CF + PI

Linear: dy/dx + Py = Q, IF = e^{int P dx}

Solution: y(IF) = int Q(IF) dx

Real-World Applications

Applications: Population growth, radioactive decay, Newtons cooling, RLC circuits, epidemiology models.

Study Tips

Tip: Identify the type of DE before solving

Tip: Practice variable separable thoroughly

Tip: Learn the integrating factor method well