Differential Equations-II Study Notes for Mechanical Engineering

1.   Linear Differential Equations

A differential equation of the form

where P(x) and Q(x) are functions of x only or constants, is known as linear differential equation.

To solve this equation, we try to convert both sides as perfect differentials multiplying the equation by another function of x say R(x).

1.1. Equations Reducible to The Linear Differential Equation

1.2 Bernoulli’s equation:

1.3. Exact Differential Equations

Given differential equation is of the form

Mdx + Ndy = 0

where, M and N are functions of x and y.

2. ORTHOGONAL TRAJECTORIES

The orthogonal trajectories of a family of curves form another family of curves such that each curve of one family cuts all the curves of the other family at right angles.

3. LINEAR DIFFERENTIAL EQUATION WITH CONSTANT COEFFICIENT

4. Complementary Function and Particular Integral

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