What is the solution for tdt+ye^{-t}dy=0 ?

The solution for tdt+ye^{-t}dy=0 is y=sqrt(-2e^tt+2e^t+c_{1)},y=-sqrt(-2e^tt+2e^t+c_{1)}

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tdt+ye^{-t}dy=0

t d t + y e^{- t} d y = 0

y = - 2 e^{t} t + 2 e^{t} + c_{1}, y = - - 2 e^{t} t + 2 e^{t} + c_{1}

Solution steps

t d t + y e^{- t} d y = 0

Solve separable ODE:

y = - 2 e^{t} t + 2 e^{t} + c_{1}, y = - - 2 e^{t} t + 2 e^{t} + c_{1}

y = - 2 e^{t} t + 2 e^{t} + c_{1}, y = - - 2 e^{t} t + 2 e^{t} + c_{1}

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What is the solution for tdt+ye^{-t}dy=0 ?
The solution for tdt+ye^{-t}dy=0 is y=sqrt(-2e^tt+2e^t+c_{1)},y=-sqrt(-2e^tt+2e^t+c_{1)}