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Lec-ODE 1

The document explains the concepts of ordinary and partial differential equations, defining ordinary differential equations as those with a single independent variable and partial differential equations as those with multiple independent variables. It discusses the order and degree of differential equations, where the order is determined by the highest derivative and the degree by the power of that derivative. Additionally, the document includes examples of eliminating constants and deriving second-order differential equations.

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13 views3 pages

Lec-ODE 1

The document explains the concepts of ordinary and partial differential equations, defining ordinary differential equations as those with a single independent variable and partial differential equations as those with multiple independent variables. It discusses the order and degree of differential equations, where the order is determined by the highest derivative and the degree by the power of that derivative. Additionally, the document includes examples of eliminating constants and deriving second-order differential equations.

Uploaded by

antilife0equation
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Differential Equation:

Equations such as:

√
√

( ) ( )

Ordinary Differential Equation: Equations which involve a single independent variable are called ordinary differential
equations.

Partial Differential Equation: Equations which involve more than one independent variable are called partial differential
equations.

Order and Degree of Differential Equations: The order of a differential equation is the order of the highest order
derivative present in the equation.

The degree of a differential equation is the power of the highest order derivative in the equation.

Ex.1) Eliminate the constants from

Putting these values in (i),we get

( )
which is a differential equation of 2nd order, obtained from the given equation after eliminating the arbitrary constants a
and b.

where c is an arbitrary constant.

Dividing (i) by (ii),

Putting these values of c in (ii),we get

( )( )

( )( )

( )( )

( ) ( )
Differentiating the given equation we get,

Dividing (i) by (ii),

( )

Putting the value of c in equation (ii),

( ){ ( )}

( )( )

( )( ( ) )

( ) ( )

( ) ( )

( ) ( )

H.W:

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