What is the solution for derivative of 2^x+2^y=2^{x+y} ?

The solution for derivative of 2^x+2^y=2^{x+y} is y=(ln(e^{\frac{2^x)/(ln(2))+c_{1}}+ln(2))}{ln(2)}

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derivative of 2^x+2^y=2^{x+y}

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

y = \frac{ln ( e ^{\frac{2 ^{x}}{l n ( 2 )} + c_{1}} + ln ( 2 ) )}{ln ( 2 )}

Solution steps

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

Solve separable ODE:

y = \frac{ln ( e ^{\frac{2 ^{x}}{l n ( 2 )} + c_{1}} + ln ( 2 ) )}{ln ( 2 )}

y = \frac{ln ( e ^{\frac{2 ^{x}}{l n ( 2 )} + c_{1}} + ln ( 2 ) )}{ln ( 2 )}

What is the solution for derivative of 2^x+2^y=2^{x+y} ?
The solution for derivative of 2^x+2^y=2^{x+y} is y=(ln(e^{\frac{2^x)/(ln(2))+c_{1}}+ln(2))}{ln(2)}