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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

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