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DEtools

  

riccatisol

  

find solutions of a first order Riccati ODE

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

riccatisol(lode, v)

Parameters

lode

-

first order differential equation

v

-

dependent variable of the lode

Description

• 

A Riccati ODE is a first order ODE of the form

  

 y'x=f0x+f1xyx+f2xyx2 

• 

The riccatisol routine determines whether the first argument is a first order Riccati ODE and, if so, returns a solution to the equation.

• 

The first argument is a differential equation in diff or D form and the second argument is the variable in the differential equation.

• 

This function is part of the DEtools package, and so it can be used in the form riccatisol(..) only after executing the command with(DEtools). However, it can always be accessed through the long form of the command by using DEtools[riccatisol](..).

Examples

withDEtools:

odexⅆⅆxzx+zx=3x2zx2

odexⅆⅆxzx+zx=3x2zx2

(1)

riccatisolode,zx

zx=13x+_C1x

(2)

odexDzx+zx=3x2zx23:

riccatisolode,zx

zx=3+ⅇ6x_C1+ⅇ6x63x

(3)

See Also

DEtools

dsolve