## 15 Reputation

4 years, 259 days

## @tomleslie Because I split the equa...

@tomleslie Because I split the equation by its coefficients.

For clarification when I type _y1 into maple in my notes this actually means y'. I just made the substitution here to make the maple code easier.

@Thomas Richard I'm trying to split it another way - Could you take a look at te reply i wrote out below?

## On paper solution...

I did this in my work book and got this result. Splitting for _y1^2, _y1 and y

_y1^2: L(x,y)_yy = 0

L(x,y)= y*A(x)+B(x)

_y1: 2L(x,y)_xy+((y/x)+1)L(x,y)_y=0

therefore by substitution  2A'(x)+(y/x+1)A(x)=0

split this up for y coefficient and those without coefficient to get

y: (1/x)A(x)=0 and 2A'(x)+A(x)=0

which then means that as A(x)=0

L(x,y)=B(x)

now solve for the rest of the terms

L(x,y)_xx+(y/x)L(x,y)_x-(y/x^2)L(x,y) = B''(x)+(y/x)B'(x)-(y/x^2)B(x)=0

take out the y coefficients

(1/x)B'(x)-(1/x^2)B(x)=0

and the other terms with no coefficients

B''(x)=0

therefore B(x)=C_1*x+C_2

put this back into y term coefficients to get

C_1/x-(1/x^2)(C_1x+c_2)=0

therefore c_2=0

and L(x,y)=C_1*x

I realise this is quite a long answer but hopefully it gives you a better idea of what I hope to achieve - and why being able to use maple to solve problems like these would be very useful for me!

## What about for Unknown L(x,y,y1)...

@Preben Alsholm Hi Preben,

This works great! I am however trying to get it for an unknown function L(x,y,y1).

How would I go about doing this?

## @Preben Alsholm so yes I think I wi...

@Preben Alsholm so yes I think I will change my origjnal query as you suggest and consider L(x,y(x),_y1(x))

:D

## @Preben Alsholm hello, thank you fo...

@Preben Alsholm hello, thank you for response.

I am currently away from computer but will be trying to work this through tomorrow morning - thank tou very much!

as for the y1, yes it is a third variable - I think I should be writing it as _y1

as for L(x,y) I am trying to find solutions at the moment for L(x,y) but in the future I wish to extend my code for L(x,y,_y1)

## Finding First integrals...

I am trying to find the first integrals of the equation. In this example I am just looking at delta(x,y), but Ideally I will be able to write a code that enables me to find delta as a function of (x,y,y') and so on.

Here is the problem I have solved and trying to put onto maple - I am a bit of a novice but as you can see it would make my calulations a lot easier if I could produce a code to solve problems like these. Thank you for any help you could possibly give.