- #1

Umayer

- 13

- 0

## Homework Statement

The equation:

[tex]\frac{dx}{dt}=\frac{t^2+1}{x+2}.[/tex]

Where the initial value is: x(0) = -2.

## Homework Equations

I believe you have to use the method of seperations of variables.

## The Attempt at a Solution

So I multiplied both sides with x+2. Then I integrated both sides with respect to t.

[tex](x+2)\frac{dx}{dt}=t^2+1[/tex]

[tex]\int(x+2)\frac{dx}{dt}\,dt=\int (t^2+1)\,dt[/tex]

[tex]\int(x+2)\,dx=\int (t^2+1)\,dt[/tex]

[tex]\frac{x^2}{2}+2x=\frac{t^3}{3}+t+C[/tex]

(Note: I've added the two constants of both sides into one constant.)

Then, I multiplied everything with 2.

[tex]x^2+4x=\frac{2}{3}t^3+2t+C'[/tex]

Where C'=2C

Now I'm not so sure how I should go further then this. Any help would be nice.