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**ammar****Member**- Registered: 2013-12-16
- Posts: 69

Use modified Euler method with (h=0.1) to solve the following differential equation:

d2y/dx2=2+y/x , Where y(1)=1 for x=1 to 1.4

How to convert second derivative to first derivative

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,671

Hi ammar;

The Euler method ( modified or not ) is usually for a first order ODE.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**ammar****Member**- Registered: 2013-12-16
- Posts: 69

Yes,but we can solve it by change the second derivative to first derivative but how to change this equation ?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,671

Yes, you can change any second order de into 2 first order or coupled ones.

I have to get offline for a bit, in the meantime watch this video. When I get back if it still is a problem then we will work on it.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**ammar****Member**- Registered: 2013-12-16
- Posts: 69

my problem is : can I assume dy/dx=z when this equation does not contain dy/dx

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,671

Hi;

Is the first equation, the second is

You left out an initial condition in your original problem.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**ammar****Member**- Registered: 2013-12-16
- Posts: 69

OK that's what I need to know

Thanks for help

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,671

What is the missing initial condition?

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**ammar****Member**- Registered: 2013-12-16
- Posts: 69

y0=1

x0=1

do you mean ?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,671

There should be a y'(x) too. But just to get the 2 equations you do not need it.

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**ammar****Member**- Registered: 2013-12-16
- Posts: 69

The equation doesn't have (dy/dx) ,I think I don't need it

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**ammar****Member**- Registered: 2013-12-16
- Posts: 69

Can I make Integral to converted to first derivative ?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Can I make Integral to converted to first derivative ?

I am not following you. What do you mean?

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**ammar****Member**- Registered: 2013-12-16
- Posts: 69

convert (d2y/dx2=2+y/x) to (dy/dx) by integral ??

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,671

Hi;

Can you copy the question exactly as it appears?

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**ammar****Member**- Registered: 2013-12-16
- Posts: 69

∫d2y/dx2=∫(2+y/x)

this lead to

dy/dx=2x+y*ln(x) , is this correct ?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,671

Oh I see what you wanted now. Sorry, I did not understand. Yes, that is what I would get.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**ammar****Member**- Registered: 2013-12-16
- Posts: 69

But I think it's would be dy/dx=2x+y*ln(x)+constant

and if we have a boundary condition (dy/dx) I will find the constant

but in the question the boundary is y(1)=1, that's not work

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,671

Yes, there would be a constant.

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**ammar****Member**- Registered: 2013-12-16
- Posts: 69

OK that's mean the integral to find the first derivative does't work

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,671

That is why I asked you what the initial conditions were. You need 2, y(1) = 1 and y'(x) = something.

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**ammar****Member**- Registered: 2013-12-16
- Posts: 69

OK thanks for help I'll try to solve it by the assumption of dy/dx=z

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Usually then you need z(0).

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**ammar****Member**- Registered: 2013-12-16
- Posts: 69

Yes but the question like i posted , any idea for solving ?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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How can you determine the constant without another initial condition?

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