- #1
KillerZ
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Homework Statement
Determine if the following differential equation is exact. If it is exact solve it.
Homework Equations
[tex]\left(\frac{1}{t} + \frac{1}{t^{2}} - \frac{y}{t^{2} + y^{2}}\right)dt + \left(ye^{y} + \frac{t}{t^{2} + y^{2}}\right)dy = 0[/tex]
The Attempt at a Solution
I am a little rusty on my partial derivatives I am not sure if this is right.
[tex]M(t, y) = \frac{1}{t} + \frac{1}{t^{2}} - \frac{y}{t^{2} + y^{2}}[/tex]
[tex]N(t, y) = ye^{y} + \frac{t}{t^{2} + y^{2}}[/tex]
[tex]\frac{\partial M}{\partial y} = -y[-(t^{2} + y^{2})^{-2}(2y)] - (t^{2} + y^{2})^{-1}[/tex]
[tex]\frac{\partial N}{\partial t} = t[-(t^{2} + y^{2})^{-2}(2t)] + (t^{2} + y^{2})^{-1}[/tex]