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

The solution for (dy)/(dx)=(3x)/(e^y) is y=ln((3x^2)/2+c_{1})

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(dy)/(dx)=(3x)/(e^y)

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

y = ln (\frac{3 x ^{2}}{2} + c_{1})

Solution steps

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

Solve separable ODE:

y = ln (\frac{3 x ^{2}}{2} + c_{1})

y = ln (\frac{3 x ^{2}}{2} + c_{1})

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

\int \frac{x ^{2} - 5 x + 16}{x ( x - 2 ) ^{2}} d x

y = 12 x, y = x^{2}

n = 0 \sum \infty (2)^{n}

\frac{d}{d x} (\frac{x ^{3}}{3})

What is the solution for (dy)/(dx)=(3x)/(e^y) ?
The solution for (dy)/(dx)=(3x)/(e^y) is y=ln((3x^2)/2+c_{1})