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DEtools

  

linearsol

  

find solutions of a first order linear ODE

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

linearsol(lode, v)

Parameters

lode

-

first order linear differential equation

v

-

dependent variable of the lode

Description

• 

The linearsol routine determines whether the first argument is a first order linear 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 function in the differential equation.

• 

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

Examples

withDEtools:

odeⅆⅆtzt+ptzt=qt

odeⅆⅆtzt+ptzt=qt

(1)

linearsolode,zt

zt=∫qtⅇ∫ptⅆtⅆt+_C1ⅇ∫ptⅆt

(2)

odeDzt+t2zt=1t+t2

odeDzt+t2zt=t2t+1

(3)

linearsolode,zt

zt=1+ⅇ13t3+1332/311/3t212/3Γ23t32/3t212/3Γ23,13t3t32/31331/312/323t311/3πΓ23t31/3t11/3Γ13,13t3t31/3+_C1ⅇ13t3

(4)

See Also

DEtools

dsolve