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sci / sci.math.symbolic / Re: what is solution of exp(x)*sin(y)+tan(y)+(exp(x)*cos(y)+x*(sec(y)^2))*y'=0

SubjectAuthor
* what is solution of exp(x)*sin(y)+tan(y)+(exp(x)*cos(y)+x*(sec(y)^2))*y'=0Dr Huang (DrHuang.com)
`* Re: what is solution of exp(x)*sin(y)+tan(y)+(exp(x)*cos(y)+x*(sec(y)^2))*y'=0Nasser M. Abbasi
 `* Re: what is solution of exp(x)*sin(y)+tan(y)+(exp(x)*cos(y)+x*(sec(y)^2))*y'=0Dr Huang (DrHuang.com)
  `* Re: what is solution of exp(x)*sin(y)+tan(y)+(exp(x)*cos(y)+x*(sec(y)^2))*y'=0Nasser M. Abbasi
   `- Re: what is solution of exp(x)*sin(y)+tan(y)+(exp(x)*cos(y)+x*(sec(y)^2))*y'=0Dr Huang (DrHuang.com)

1
Subject: what is solution of exp(x)*sin(y)+tan(y)+(exp(x)*cos(y)+x*(sec(y)^2))*y'=0
From: Dr Huang (DrHuang.co
Newsgroups: sci.math.symbolic
Date: Wed, 4 Oct 2023 12:46 UTC
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Subject: what is solution of exp(x)*sin(y)+tan(y)+(exp(x)*cos(y)+x*(sec(y)^2))*y'=0
From: drhuang57@gmail.com (Dr Huang (DrHuang.com))
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wolfram cannot give a simple solution? why is its solution so complicated? Is it a bug?

mathhand.com gives a simple solution and auto plot the solution

Subject: Re: what is solution of exp(x)*sin(y)+tan(y)+(exp(x)*cos(y)+x*(sec(y)^2))*y'=0
From: Nasser M. Abbasi
Newsgroups: sci.math.symbolic
Organization: A noiseless patient Spider
Date: Thu, 5 Oct 2023 07:35 UTC
References: 1
Path: eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: nma@12000.org (Nasser M. Abbasi)
Newsgroups: sci.math.symbolic
Subject: Re: what is solution of
exp(x)*sin(y)+tan(y)+(exp(x)*cos(y)+x*(sec(y)^2))*y'=0
Date: Thu, 5 Oct 2023 02:35:24 -0500
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On 10/4/2023 7:46 AM, Dr Huang (DrHuang.com) wrote:
> wolfram cannot give a simple solution? why is its solution so complicated? Is it a bug?
>
> mathhand.com gives a simple solution and auto plot the solution
>
>

What is the solution you obtained?

I solved it and got

exp(x)*sin(y(x)) + x*tan(y(x)) = c_1

Where c_1 is constant of integration. Here is my solution

https://12000.org/tmp/10052023/main.pdf

This is an easy ode to solve as it is exact ode.

Mathematica 13.3.1 gives complicated answer because its answer is explicit.

Mathematica DSolve does not have an option to ask for an implicit solution
like with Maple's dsolve.

ode = Exp[x]*Sin[y[x]] + Tan[y[x]] + (Exp[x]*Cos[y[x]] + x*(Sec[y[x]]^2))*y'[x] == 0;
DSolve[ode, y[x], x]

The answer is long, because it tried to solve for y from the solution above.
That is all. It will be nice if DSolve has an option asking for implicit
solution to an ode.

--Nasser

Subject: Re: what is solution of exp(x)*sin(y)+tan(y)+(exp(x)*cos(y)+x*(sec(y)^2))*y'=0
From: Dr Huang (DrHuang.co
Newsgroups: sci.math.symbolic
Date: Fri, 6 Oct 2023 00:17 UTC
References: 1 2
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Subject: Re: what is solution of exp(x)*sin(y)+tan(y)+(exp(x)*cos(y)+x*(sec(y)^2))*y'=0
From: drhuang57@gmail.com (Dr Huang (DrHuang.com))
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On Thursday, 5 October 2023 at 18:35:28 UTC+11, Nasser M. Abbasi wrote:
> On 10/4/2023 7:46 AM, Dr Huang (DrHuang.com) wrote:
> > wolfram cannot give a simple solution? why is its solution so complicated? Is it a bug?
> >
> > mathhand.com gives a simple solution and auto plot the solution
> >
> >
> What is the solution you obtained?
>
> I solved it and got
>
> exp(x)*sin(y(x)) + x*tan(y(x)) = c_1
>
> Where c_1 is constant of integration. Here is my solution
>
> https://12000.org/tmp/10052023/main.pdf
thanks

>
> This is an easy ode to solve as it is exact ode.
you are right, this is an easy ode to solve. but wolfram make a simple solution to complicated.

>
> Mathematica 13.3.1 gives complicated answer because its answer is explicit.
>
> Mathematica DSolve does not have an option to ask for an implicit solution
> like with Maple's dsolve.
>
> ode = Exp[x]*Sin[y[x]] + Tan[y[x]] + (Exp[x]*Cos[y[x]] + x*(Sec[y[x]]^2))*y'[x] == 0;
> DSolve[ode, y[x], x]
>
> The answer is long, because it tried to solve for y from the solution above.
> That is all. It will be nice if DSolve has an option asking for implicit
> solution to an ode.
how to check its solution?

>
> --Nasser
Thanks

--------------
mathHand.com

Subject: Re: what is solution of exp(x)*sin(y)+tan(y)+(exp(x)*cos(y)+x*(sec(y)^2))*y'=0
From: Nasser M. Abbasi
Newsgroups: sci.math.symbolic
Organization: A noiseless patient Spider
Date: Fri, 6 Oct 2023 02:59 UTC
References: 1 2 3
Path: eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: nma@12000.org (Nasser M. Abbasi)
Newsgroups: sci.math.symbolic
Subject: Re: what is solution of
exp(x)*sin(y)+tan(y)+(exp(x)*cos(y)+x*(sec(y)^2))*y'=0
Date: Thu, 5 Oct 2023 21:59:02 -0500
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On 10/5/2023 7:17 PM, Dr Huang (DrHuang.com) wrote:

>> The answer is long, because it tried to solve for y from the solution above.
>> That is all. It will be nice if DSolve has an option asking for implicit
>> solution to an ode.

> how to check its solution?
>

The method to check solution for ode in Mathematica is given in

https://reference.wolfram.com/language/howto/CheckTheResultsOfDSolve.html

Basically, you do

ode=y'[x]+y[x]==0;
sol=DSolve[ode,y,x];
ode/.sol//Simplify

{True}

Since it returned True, then the solution is correct, as it means it
satisfies the ode.

For your example, it is the same thing

ode = Exp[x]*Sin[y[x]] + Tan[y[x]] + (Exp[x]*Cos[y[x]] + x*(Sec[y[x]]^2))*y'[x] == 0;
sol = DSolve[ode, y, x];
ode /. sol // Simplify

But since the solution is very complicated, it was taking too long to finish
for me to wait so I stopped it after 10 minutes.

Note to use the above, you need to use the format DSolve[ode, y, x] and
not DSolve[ode, y[x], x];

--Nasser

Subject: Re: what is solution of exp(x)*sin(y)+tan(y)+(exp(x)*cos(y)+x*(sec(y)^2))*y'=0
From: Dr Huang (DrHuang.co
Newsgroups: sci.math.symbolic
Date: Fri, 6 Oct 2023 03:25 UTC
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Subject: Re: what is solution of exp(x)*sin(y)+tan(y)+(exp(x)*cos(y)+x*(sec(y)^2))*y'=0
From: drhuang57@gmail.com (Dr Huang (DrHuang.com))
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On Friday, 6 October 2023 at 13:59:08 UTC+11, Nasser M. Abbasi wrote:
> On 10/5/2023 7:17 PM, Dr Huang (DrHuang.com) wrote:
>
> >> The answer is long, because it tried to solve for y from the solution above.
> >> That is all. It will be nice if DSolve has an option asking for implicit
> >> solution to an ode.
>
> > how to check its solution?
> >
> The method to check solution for ode in Mathematica is given in
>
> https://reference.wolfram.com/language/howto/CheckTheResultsOfDSolve.html
>
> Basically, you do
>
> ode=y'[x]+y[x]==0;
> sol=DSolve[ode,y,x];
> ode/.sol//Simplify
>
> {True}
>
> Since it returned True, then the solution is correct, as it means it
> satisfies the ode.
>
> For your example, it is the same thing
> ode = Exp[x]*Sin[y[x]] + Tan[y[x]] + (Exp[x]*Cos[y[x]] + x*(Sec[y[x]]^2))*y'[x] == 0;
> sol = DSolve[ode, y, x];
> ode /. sol // Simplify
>
> But since the solution is very complicated, it was taking too long to finish
> for me to wait so I stopped it after 10 minutes.
>
> Note to use the above, you need to use the format DSolve[ode, y, x] and
> not DSolve[ode, y[x], x];
>
> --Nasser
How to check its solution with wolfram alpha?
Can it be easy to check by a click? as check solution by a click the test button in mathhand.com?

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