- #1

- 17

- 0

## Homework Statement

Solve IVP (Initial Value Problem): [itex](2xy+sin(x))dx+(x^{2}+1)dy=0, y(0)=2[/itex]

Is the solution unique? Motivate why!

## Homework Equations

Relevant equations for solving the exact equation...

## The Attempt at a Solution

I can solve this without any trouble. Since the answer is an implicit solution, I get:

[itex]F(x,y)=x^{2}y-cos(x)+y= C [/itex]

Putting in the IVP value I get for y:

[itex]y(x)=\frac{1+cos(x)}{x^{2}+1}[/itex]

Now, to the question, is this solution unique? Why? Why not? And how does it relate to implicit solutions (here, exact differential equation)?

What about if this IVP was a separable, or a linear differential equation?

I am thankful for any hints, because this one got me really thinking...