What is the solution for (dx)/(0.5+0.8x)=(dy)/(1.5-0.8y) ?

The solution for (dx)/(0.5+0.8x)=(dy)/(1.5-0.8y) is y=-(c_{1})/(0.8x+0.5)+1.875

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(dx)/(0.5+0.8x)=(dy)/(1.5-0.8y)

\frac{d x}{0.5 + 0.8 x} = \frac{d y}{1.5 - 0.8 y}

y = - \frac{c _{1}}{0.8 x + 0.5} + 1.875

Solution steps

\frac{d x}{0.5 + 0.8 x} = \frac{d y}{1.5 - 0.8 y}

Solve separable ODE:

y = - \frac{c _{1}}{0.8 x + 0.5} + 1.875

y = - \frac{c _{1}}{0.8 x + 0.5} + 1.875

y^{^{'}} + 4 y = \frac{4}{3}

x \frac{d y}{d x} = \frac{e ^{x}}{e ^{y}}

e^{4 x} e^{2 y} \frac{d x}{d y} - e^{- 3 y} = 0

x^{2} y^{^{'}} = - 3 y

\frac{d y}{d x} = \frac{x}{2 y}

What is the solution for (dx)/(0.5+0.8x)=(dy)/(1.5-0.8y) ?
The solution for (dx)/(0.5+0.8x)=(dy)/(1.5-0.8y) is y=-(c_{1})/(0.8x+0.5)+1.875