What is the solution for (dx)/(dt)= t/(xe^{t+2x)} ?

The solution for (dx)/(dt)= t/(xe^{t+2x)} is x=(\W((-te^{-t}*4-e^{-t}*4+c_{1})/e))/(2)+1/2

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(dx)/(dt)= t/(xe^{t+2x)}

\frac{d x}{d t} = \frac{t}{x e ^{t + 2 x}}

x = \frac{W ( \frac{- t e ^{- t} \cdot 4 - e ^{- t} \cdot 4 + c _{1}}{e} )}{2} + \frac{1}{2}

Solution steps

\frac{d x}{d t} = \frac{t}{x e ^{t + 2 x}}

Solve separable ODE:

x = \frac{W ( \frac{- t e ^{- t} \cdot 4 - e ^{- t} \cdot 4 + c _{1}}{e} )}{2} + \frac{1}{2}

x = \frac{W ( \frac{- t e ^{- t} \cdot 4 - e ^{- t} \cdot 4 + c _{1}}{e} )}{2} + \frac{1}{2}

y^{^{'}} + sin (x) y = sin (x), y (0) = π

(87) (8 - 4)

\int \frac{15}{2} t + 8 e^{- t} d t

\int sec (u) d u

f (x) = \frac{2 x + 1}{x + 3}

What is the solution for (dx)/(dt)= t/(xe^{t+2x)} ?
The solution for (dx)/(dt)= t/(xe^{t+2x)} is x=(\W((-te^{-t}*4-e^{-t}*4+c_{1})/e))/(2)+1/2