What is the solution for (dy)/(dx)=(e^x+7)^2 ?

The solution for (dy)/(dx)=(e^x+7)^2 is y= 1/2 e^{2x}+14e^x+49x+c_{1}

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(dy)/(dx)=(e^x+7)^2

\frac{d y}{d x} = (e^{x} + 7)^{2}

y = \frac{1}{2} e^{2 x} + 14 e^{x} + 49 x + c_{1}

Solution steps

\frac{d y}{d x} = (e^{x} + 7)^{2}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = (e^{x} + 7)^{2}

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

then

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

y = \int (e^{x} + 7)^{2} d x

\int (e^{x} + 7)^{2} d x = \frac{1}{2} e^{2 x} + 14 e^{x} + 49 x + c_{1}

y = \frac{1}{2} e^{2 x} + 14 e^{x} + 49 x + c_{1}

y = x^{2} cos (\frac{4}{x})

f (x) = x^{4} + 2 e^{x}, (0, 2)

(sin (x))^{2}

x \to 0 + lim (- x + 5)

e^{- 3 x}

What is the solution for (dy)/(dx)=(e^x+7)^2 ?
The solution for (dy)/(dx)=(e^x+7)^2 is y= 1/2 e^{2x}+14e^x+49x+c_{1}