What is the solution for (dy)/(dx)=((3x+10)e^{-2y})/(x^2+6x+8) ?

The solution for (dy)/(dx)=((3x+10)e^{-2y})/(x^2+6x+8) is y=(ln(2ln((x+2)^2(x+4))+c_{1}))/2

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(dy)/(dx)=((3x+10)e^{-2y})/(x^2+6x+8)

\frac{d y}{d x} = \frac{( 3 x + 10 ) e ^{- 2 y}}{x ^{2} + 6 x + 8}

y = \frac{ln ( 2 ln ( ( x + 2 ) ^{2} ( x + 4 ) ) + c _{1} )}{2}

Solution steps

\frac{d y}{d x} = \frac{( 3 x + 10 ) e ^{- 2 y}}{x ^{2} + 6 x + 8}

Solve separable ODE:

y = \frac{ln ( 2 ln ( ( x + 2 ) ^{2} ( x + 4 ) ) + c _{1} )}{2}

y = \frac{ln ( 2 ln ( ( x + 2 ) ^{2} ( x + 4 ) ) + c _{1} )}{2}

\frac{d x}{d t} = 40 - \frac{x}{100}, x = 3000, t = 0

(3 x + 8) (y^{2} + 4) d x - 4 y (x^{2} + 5 x + 6) d y = 0, y (1) = 2

\frac{d y}{d t} = 3 y (1 - y)

e^{2 x} y^{2} y^{^{'}} = 1

\frac{d x}{d t} - 4 t x = 0

What is the solution for (dy)/(dx)=((3x+10)e^{-2y})/(x^2+6x+8) ?
The solution for (dy)/(dx)=((3x+10)e^{-2y})/(x^2+6x+8) is y=(ln(2ln((x+2)^2(x+4))+c_{1}))/2