What is the solution for (dy)/(dx)=500e^{1/10 ln(625/500)50} ?

The solution for (dy)/(dx)=500e^{1/10 ln(625/500)50} is y= 390625/256 x+c_{1}

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(dy)/(dx)=500e^{1/10 ln(625/500)50}

\frac{d y}{d x} = 500 e^{\frac{1}{10} l n (\frac{625}{500}) 50}

y = \frac{390625}{256} x + c_{1}

Solution steps

\frac{d y}{d x} = 500 e^{\frac{1}{10} l n (\frac{625}{500}) 50}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = 500 e^{\frac{1}{10} l n (\frac{625}{500}) \cdot 50}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int 500 e^{\frac{1}{10} l n (\frac{625}{500}) \cdot 50} d x

\int 500 e^{\frac{1}{10} l n (\frac{625}{500}) \cdot 50} d x = \frac{390625}{256} x + c_{1}

y = \frac{390625}{256} x + c_{1}

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What is the solution for (dy)/(dx)=500e^{1/10 ln(625/500)50} ?
The solution for (dy)/(dx)=500e^{1/10 ln(625/500)50} is y= 390625/256 x+c_{1}