What is the solution for (dy)/(dx)=3xe^{3x+y} ?

The solution for (dy)/(dx)=3xe^{3x+y} is y=-ln(-e^{3x}x+1/3 e^{3x}-c_{1})

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(dy)/(dx)=3xe^{3x+y}

\frac{d y}{d x} = 3 x e^{3 x + y}

y = - ln (- e^{3 x} x + \frac{1}{3} e^{3 x} - c_{1})

Solution steps

\frac{d y}{d x} = 3 x e^{3 x + y}

Solve separable ODE:

y = - ln (- e^{3 x} x + \frac{1}{3} e^{3 x} - c_{1})

y = - ln (- e^{3 x} x + \frac{1}{3} e^{3 x} - c_{1})

y e^{2 x} - (1 + e^{2 x}) \frac{d y}{d x} = 0

\frac{d y}{d x} + y cos (x) = 8 cos (x)

y^{^{'}} = y - (\frac{1}{1000}) y^{2}

\frac{d y}{d x} = cos^{2} (x) cos^{2} (2 y)

y^{^{'}} = \frac{x}{y}, y (0) = 0

What is the solution for (dy)/(dx)=3xe^{3x+y} ?
The solution for (dy)/(dx)=3xe^{3x+y} is y=-ln(-e^{3x}x+1/3 e^{3x}-c_{1})