# Mathematica Disagrees with ME

Mathematica Disagrees with ME!!!!!!!!!!

## Homework Statement

(2xy-5)dx+(x^2+y^2)dy=0 y(3)=1

## The Attempt at a Solution

Ive solved this by hand and now where required to get Mathematica to solve to.
My solution: $$-17/3=x^2y-5x+y^3/3$$
I've attached what mathematica has done. Now the question
Am I wrong ?
Is my code wrong?
Is mathematica wrong?

Thanks

P.S I rearranged to this form to sick in mathematica:
dy/dx=(-2xy+5)/(x^2+y^2)

#### Attachments

• mathematica.png
47.3 KB · Views: 394

Mark44
Mentor

Your thumbnail is too small for me to be able to read. In any case, your work is correct. You can verify it by doing two things:
1) Checking that the initial condition is satisfied; i.e., that when x = 3 and y = 1, then x2y - 5x + y3/3 = -17/3 is a true statement.
2) Differentiating the equation x2y - 5x + y3/3 = -17/3 implicitly to arrive at the differential equation dy/dx = (5 - 2xy)/(x2 + y2).

Checking a solution to a differential equation is something you should do as a matter of course. You've already done all the hard work. It's only a little more work to verify that your work is correct.

good to know that I did it right by hand, do you know the correct mathematica code so that it will do it.

Thanks

Mark44
Mentor

No. I don't have mathematica.

lurflurf
Homework Helper

That mathematica output looks correct. The cubic in y has been factored, what kind of output were you expecting?

one the same as mine---- is that not possible here?

I like Serena
Homework Helper

## Homework Statement

(2xy-5)dx+(x^2+y^2)dy=0 y(3)=1

## The Attempt at a Solution

Ive solved this by hand and now where required to get Mathematica to solve to.
My solution: $$-17/3=x^2y-5x+y^3/3$$
I've attached what mathematica has done. Now the question
Am I wrong ?
Is my code wrong?
Is mathematica wrong?

Thanks

P.S I rearranged to this form to sick in mathematica:
dy/dx=(-2xy+5)/(x^2+y^2)

Mathematica did a little more work than you did.

What you have is a third order equation of y.
Mathematica solved it to be of the form y = f(x).
I haven't checked it, but it looks about right: 1 real solution and 2 imaginary ones.
Presumably you can rewrite the first solution to match your solution.

I'm not a Mathematica specialist, but I suspect it is not equipped to output the kind of solution you gave.

SteamKing
Staff Emeritus
Homework Helper

pat666: your solution from sec. 3 of the OP does not satisfy the initial condition y(3)=1

SteamKing
Staff Emeritus