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

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

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(dx)/(dt)= 1/((x+t+1))

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

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

Solution steps

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

Solve exact ODE:

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

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

(- \frac{1}{5}, \frac{1}{3}), (\frac{4}{5}, - \frac{5}{3})

\frac{\partial}{\partial y} (4 x ln (x y))

\frac{d y}{d x} = \frac{5 x ^{2} + y ^{2}}{x y}

\frac{d y}{d t} + \frac{1}{t} y = \frac{6}{t}, y (1) = 6

\int \frac{sin ( \frac{x}{2} )}{cos ^{2} ( \frac{x}{2} )} d x

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