What is the solution for (dx)/(dt)=e^xtcos(t) ?

The solution for (dx)/(dt)=e^xtcos(t) is x=-ln(-tsin(t)-cos(t)-c_{1})

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(dx)/(dt)=e^xtcos(t)

\frac{d x}{d t} = e^{x} t cos (t)

x = - ln (- t sin (t) - cos (t) - c_{1})

Solution steps

\frac{d x}{d t} = e^{x} t cos (t)

Solve separable ODE:

x = - ln (- t sin (t) - cos (t) - c_{1})

x = - ln (- t sin (t) - cos (t) - c_{1})

What is the solution for (dx)/(dt)=e^xtcos(t) ?
The solution for (dx)/(dt)=e^xtcos(t) is x=-ln(-tsin(t)-cos(t)-c_{1})