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dalembertsol

  

find solutions of a first order ODE of d'Alembert type

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

dalembertsol(lode, v)

Parameters

lode

-

first order differential equation

v

-

dependent variable of the lode

Description

• 

The dalembertsol routine determines whether the first argument is a first order ODE of d'Alembert type and, if so, returns a solution to the equation.

• 

The first argument is a differential equation in diff or D form. The second argument (required cannot be inferred from the differential equation) is the variable in the differential equation.

• 

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

Examples

withDEtools:

dAlembert_odeyx=xfⅆⅆxyx+gⅆⅆxyx

dAlembert_odeyx=xfⅆⅆxyx+gⅆⅆxyx

(1)

dalembertsoldAlembert_ode,yx

yx=xRootOf_Zf_Z+gRootOf_Zf_Z,x_T=ⅇ∫ⅆⅆ_Tf_T_Tf_Tⅆ_T∫ⅆⅆ_Tg_Tⅇ∫ⅆⅆ_Tf_T_Tf_Tⅆ_T_Tf_Tⅆ_T+_C1,yx_T=ⅇ∫ⅆⅆ_Tf_T_Tf_Tⅆ_T∫ⅆⅆ_Tg_Tⅇ∫ⅆⅆ_Tf_T_Tf_Tⅆ_T_Tf_Tⅆ_T+_C1f_T+g_T

(2)

See Also

DEtools

dsolve

odeadvisor/dAlembert

RootOf