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

The solution for (dy)/(dx)=1+2/((y-x)e^{3(y-x))} is y=(\W((c_{1}+18x)/e))/(3)+x+1/3

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(dy)/(dx)=1+2/((y-x)e^{3(y-x))}

\frac{d y}{d x} = 1 + \frac{2}{( y - x ) e ^{3 (y - x)}}

y = \frac{W ( \frac{c _{1} + 18 x}{e} )}{3} + x + \frac{1}{3}

Solution steps

\frac{d y}{d x} = 1 + \frac{2}{( y - x ) e ^{3 (y - x)}}

Solve exact ODE:

y = \frac{W ( \frac{c _{1} + 18 x}{e} )}{3} + x + \frac{1}{3}

y = \frac{W ( \frac{c _{1} + 18 x}{e} )}{3} + x + \frac{1}{3}

x \to 1 lim (ln (3) + e^{x})

\frac{d}{d x} (ln (4 x - 2 y + 6))

y^{^{''}} + 9 y = 3 sin (2 x)

x \to 4 - lim (2)

y^{^{''}} + 2 y^{^{'}} = 8

What is the solution for (dy)/(dx)=1+2/((y-x)e^{3(y-x))} ?
The solution for (dy)/(dx)=1+2/((y-x)e^{3(y-x))} is y=(\W((c_{1}+18x)/e))/(3)+x+1/3