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Question: How i can give assumption to a ODE equation and for each assumption there is a different outcome?

Question:How i can give assumption to a ODE equation and for each assumption there is a different outcome?

salim-barzani 1785 Maple 2024
ode assumptions dsolve differential-equations duplicate-question
October 25 2024
1

i can do one by one for all case but i am intrested for this idea how we can do that for each equation automatically calculate all case without use one by one case ?
there is any other shorter way for get solution of this mw

all_case.mw

> 

restart
> 

with(PDEtools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

with(DEtools)
> 

S := diff(G(xi), xi) = G(xi)^2+A*G(xi)+B

diff(G(xi), xi) = G(xi)^2+A*G(xi)+B

 (2)
> 

S1 := dsolve(S, G(xi))

G(xi) = -(1/2)*A-(1/2)*tanh((1/2)*(A^2-4*B)^(1/2)*(c__1+xi))*(A^2-4*B)^(1/2)

 (3)
> 

A := 0

0

 (4)
> 

S

diff(G(xi), xi) = G(xi)^2+B

 (5)
> 

dsolve(S, G(xi))

G(xi) = tan(B^(1/2)*(c__1+xi))*B^(1/2)

 (6)
> 

restart
> 

NULL
> 

with(PDEtools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (7)
> 

with(DEtools)
> 

S := diff(G(xi), xi) = G(xi)^2+A*G(xi)+B

diff(G(xi), xi) = G(xi)^2+A*G(xi)+B

 (8)
> 

B := 0

0

 (9)
> 

S1 := dsolve(S, G(xi))

G(xi) = A/(-1+exp(-A*xi)*c__1*A)

 (10)
> 

NULL
> 

restart
> 

NULL
> 

with(PDEtools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (11)
> 

with(DEtools)
> 

S := diff(G(xi), xi) = G(xi)^2+A*G(xi)+B

diff(G(xi), xi) = G(xi)^2+A*G(xi)+B

 (12)
> 

B := 0; A := 0

0

  

0

 (13)
> 

S1 := dsolve(S, G(xi))

G(xi) = 1/(-xi+c__1)

 (14)
 

NULL

Download find_all_case_solution_of_ode_.mw
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