What is the solution for x(dx)/(dt)-t(2x+1)=0 ?

The solution for x(dx)/(dt)-t(2x+1)=0 is x=-(\W(-1/(e^{-c_{1)+2t^2}}))/2-1/2

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x(dx)/(dt)-t(2x+1)=0

x \frac{d x}{d t} - t (2 x + 1) = 0

x = - \frac{W ( - \frac{1}{e ^{- c_{1} + 2 t^{2}}} )}{2} - \frac{1}{2}

Solution steps

x \frac{d x}{d t} - t (2 x + 1) = 0

Solve Bernoulli ODE:

x = - \frac{W ( - \frac{1}{e ^{- c_{1} + 2 t^{2}}} )}{2} - \frac{1}{2}

x = - \frac{W ( - \frac{1}{e ^{- c_{1} + 2 t^{2}}} )}{2} - \frac{1}{2}

y^{^{'}} = \frac{x y ^{2}}{1 + x ^{2}}

\frac{d y}{d t} + 7 y = 0

y^{^{'}} = (- 3 \cdot 1 0^{- 12}) y^{4}

f^{^{'}} (x) x = 3 f (x)

\frac{d y}{d x} = \frac{y - 3}{2 x + 1}, y (0) = 4

What is the solution for x(dx)/(dt)-t(2x+1)=0 ?
The solution for x(dx)/(dt)-t(2x+1)=0 is x=-(\W(-1/(e^{-c_{1)+2t^2}}))/2-1/2