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Non-Trivial Symbolic Solutions

Anousheh
Regular Member

Non-Trivial Symbolic Solutions

Hello,

Please help me to solve symbolically:

y"+4y=0 (non-trivial solution)

Thank you so much for the time and help.

11 REPLIES 11

Re: Non-Trivial Symbolic Solutions

Solve for what?

Clipboard01.jpg

Mike

Re: Non-Trivial Symbolic Solutions

Thank you Mike,

The condition y(0)=1 should be satisfied.

The correct answer should be y=Cos(2x)

Please help if you can

Thanks

Re: Non-Trivial Symbolic Solutions

Hi Anousheh

I don't know if the symbolic engine can handle this type of question as the result is somewhat indeterminate

From the Odesolve part of the attached file you can obtain a numerical solution which shows some form of trigonometric function.

Varying the initial conditions y'(t0)=y'0 and y(t1)=y1 in the odesolve block will give solutions including sin(t), cos(t) and many other variations.

The symbolic calculations following also show the possibilities but there will be many more possible valid solutions.

Re: Non-Trivial Symbolic Solutions

Thank you A Westerman,

I have the condition y(0)=1 that should be satisfied.

The correct answer is y=Cos(2x)

Please help

Thank you

Re: Non-Trivial Symbolic Solutions

Anousheh Rouzbehani wrote:

Thank you A Westerman,

I have the condition y(0)=1 that should be satisfied.

The correct answer is y=Cos(2x)

Please help

Thank you

Sorry, but must be two conditions - the ODE has a 2-d order.

Re: Non-Trivial Symbolic Solutions

OK

Let's say the second condition is: y'(0)=0.5

Thanks

Re: Non-Trivial Symbolic Solutions

Hello A Westerman,

Thanks again for your valuable information.

Please see the following ODE:

y'=F(x,y) [y prime]

with the prescribed initial condition y(x0)=y0

How do we solve this kind of ODE?

Thanks so much.

Anousheh

Re: Non-Trivial Symbolic Solutions

Hi Anousheh,

difficult to know exactly what you need. Can you post an example of the function(s) you are interested in - (save as ver 12 or lower as I only have access to ver 12).

The quicksheets tend to be a good starting resource & may give you an insight into what is possible.

one option from them attached as a simple example.

regards

Andy

Re: Non-Trivial Symbolic Solutions

Anousheh Rouzbehani wrote:

Hello,

Please help me to solve symbolically:

y"+4y=0 (non-trivial solution)

Thank you so much for the time and help.

C1*sin(2x)+C2*cos(2x)

Sorry,

what is it "non-trivial solution"?

Re: Non-Trivial Symbolic Solutions

Thank you so much.

The correct answer should be y=Cos(2x), this satisfies the condition y(0)=1

Can you help please?

Re: Non-Trivial Symbolic Solutions

Anousheh Rouzbehani wrote:

Thank you so much.

The correct answer should be y=Cos(2x), this satisfies the condition y(0)=1

Can you help please?

Sorry, but what help do you need?

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