Differential Equations-II Study Notes for Mechanical Engineering

By Akhil Gupta|Updated : November 12th, 2020

1.   Linear Differential Equations

A differential equation of the form

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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).

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1.1. Equations Reducible to The Linear Differential Equation

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1.2 Bernoulli’s equation:

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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.

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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.

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3. LINEAR DIFFERENTIAL EQUATION WITH CONSTANT COEFFICIENT

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4. Complementary Function and Particular Integral

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