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DEtools

  

bernoullisol

  

find solutions of a Bernoulli first order ODE

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

bernoullisol(lode, v)

Parameters

lode

-

first order differential equation

v

-

dependent variable of the lode

Description

• 

The bernoullisol routine determines if the first argument is a first order ODE of Bernoulli type and, if so, returns a solution to the Bernoulli equation.

• 

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

• 

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

Examples

withDEtools:

odeⅆⅆtzt+ptzt=qtzt2

odeⅆⅆtzt+ptzt=qtzt2

(1)

bernoullisolode,zt

zt=ⅇptⅆtⅇptⅆtqtⅆt+_C1

(2)

odeⅆⅆtzt+tzt=qtztn:

bernoullisolode,zt

zt=ⅇt2n2n1ⅇt22n1nⅇt2n2ⅇt22qtⅆt+_C1+ⅇt2n2ⅇt22qtⅆt1n1

(3)

odeDzt+tzt=tztn:

bernoullisolode,zt

zt=11+ⅇt2n12_C11n1

(4)

See Also

DEtools

dsolve