What is the solution for ((e^{3x}+3)e^y)dy-((e^y-4)e^{3x})dx=0 ?

The solution for ((e^{3x}+3)e^y)dy-((e^y-4)e^{3x})dx=0 is y=ln(c_{1}\sqrt[3]{e^{3x}+3}+4)

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((e^{3x}+3)e^y)dy-((e^y-4)e^{3x})dx=0

((e^{3 x} + 3) e^{y}) d y - ((e^{y} - 4) e^{3 x}) d x = 0

Solution steps

((e^{3 x} + 3) e^{y}) d y - ((e^{y} - 4) e^{3 x}) d x = 0

Solve separable ODE:

\frac{d y}{d x} y = (6 x - 4)^{3}

2 = \frac{1}{10} y + (100 \cdot 1 0^{- 3}) y^{^{'}}

\frac{d y}{d x} = x^{3} y^{2} - x y^{2}

\frac{d y}{d t} = 2 t y^{2} + 3 t^{2} y^{2}

\frac{d}{d t} (v (t) e^{k t}) = g e^{k t}

What is the solution for ((e^{3x}+3)e^y)dy-((e^y-4)e^{3x})dx=0 ?
The solution for ((e^{3x}+3)e^y)dy-((e^y-4)e^{3x})dx=0 is y=ln(c_{1}\sqrt[3]{e^{3x}+3}+4)