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})

\frac{d y}{d x} + 9 x^{2} y = 27 x^{2}

\frac{d x}{d t} = 18 - \frac{18}{100} x

y^{^{'}} = - \frac{x - 2}{y - 6}, y (3) = 0

3.03 y^{^{'}} + 0.755 y = 6.05

3 (1 + x) \frac{d y}{d x} = 2 x y (y^{3} - 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})