What is the solution for (dy)/(dx)=(e^x+5)^2 ?

The solution for (dy)/(dx)=(e^x+5)^2 is y= 1/2 e^{2x}+10e^x+25x+c_{1}

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(dy)/(dx)=(e^x+5)^2

\frac{d y}{d x} = (e^{x} + 5)^{2}

y = \frac{1}{2} e^{2 x} + 10 e^{x} + 25 x + c_{1}

Solution steps

\frac{d y}{d x} = (e^{x} + 5)^{2}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = (e^{x} + 5)^{2}

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

then

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

y = \int (e^{x} + 5)^{2} d x

\int (e^{x} + 5)^{2} d x = \frac{1}{2} e^{2 x} + 10 e^{x} + 25 x + c_{1}

y = \frac{1}{2} e^{2 x} + 10 e^{x} + 25 x + c_{1}

What is the solution for (dy)/(dx)=(e^x+5)^2 ?
The solution for (dy)/(dx)=(e^x+5)^2 is y= 1/2 e^{2x}+10e^x+25x+c_{1}