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

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

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(dy)/(dx)=(x-3)e^{(-2y)}

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

y = \frac{ln ( x ^{2} - 6 x + c _{1} )}{2}

Solution steps

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

Solve separable ODE:

y = \frac{ln ( x ^{2} - 6 x + c _{1} )}{2}

y = \frac{ln ( x ^{2} - 6 x + c _{1} )}{2}

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- 4 t^{2} y^{^{''}} + 5 t y^{^{'}} - 2 y = 0

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