What is the solution for (dy)/(dx)=(x+1)/(e^{3y+9)} ?

The solution for (dy)/(dx)=(x+1)/(e^{3y+9)} is y=(ln((3x^2)/2+3x+c_{1}))/(3)-3

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(dy)/(dx)=(x+1)/(e^{3y+9)}

\frac{d y}{d x} = \frac{x + 1}{e ^{3 y + 9}}

y = \frac{ln ( \frac{3 x ^{2}}{2} + 3 x + c _{1} )}{3} - 3

Solution steps

\frac{d y}{d x} = \frac{x + 1}{e ^{3 y + 9}}

Solve separable ODE:

y = \frac{ln ( \frac{3 x ^{2}}{2} + 3 x + c _{1} )}{3} - 3

y = \frac{ln ( \frac{3 x ^{2}}{2} + 3 x + c _{1} )}{3} - 3

x \to 2 lim ((10 - 3 x)^{2})

\int_{1}^{36} e^{x} d x

y = \frac{9}{9 x - x ^{2}}, x = 1, x = 7.5

\int_{- 1}^{1} 2 - x^{2} d x

\int_{- 1}^{2} x^{2} - 2 x d x

What is the solution for (dy)/(dx)=(x+1)/(e^{3y+9)} ?
The solution for (dy)/(dx)=(x+1)/(e^{3y+9)} is y=(ln((3x^2)/2+3x+c_{1}))/(3)-3