What is the solution for (dy}{dx}=\frac{3e^x)/y ?

The solution for (dy}{dx}=\frac{3e^x)/y is y=sqrt(6e^x+c_{1)},y=-sqrt(6e^x+c_{1)}

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(dy}{dx}=\frac{3e^x)/y

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

y = 6 e^{x} + c_{1}, y = - 6 e^{x} + c_{1}

Solution steps

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

Solve separable ODE:

y = 6 e^{x} + c_{1}, y = - 6 e^{x} + c_{1}

y = 6 e^{x} + c_{1}, y = - 6 e^{x} + c_{1}

y^{2} y^{^{'}} = x - 2

\frac{d y}{d x} - \frac{2}{x} y - \frac{1}{x y} = 0

\frac{d y}{d t} = 0.1 y, y (0) = 600, t = 5

sin (3 x) d x + 4 y cos^{2} (3 x) d y = 0

\frac{d y}{d x} = \frac{2 x}{- 8 y - 6}, y (0) = - 8

What is the solution for (dy}{dx}=\frac{3e^x)/y ?
The solution for (dy}{dx}=\frac{3e^x)/y is y=sqrt(6e^x+c_{1)},y=-sqrt(6e^x+c_{1)}