What is the solution for (dy)/(dx)=sqrt(7y)e^{x+8} ?

The solution for (dy)/(dx)=sqrt(7y)e^{x+8} is y=(7e^{16+2x})/4+(sqrt(7)c_{1}e^{x+8})/2+(c_{1}^2)/4

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(dy)/(dx)=sqrt(7y)e^{x+8}

\frac{d y}{d x} = 7 y e^{x + 8}

y = \frac{7 e ^{16 + 2 x}}{4} + \frac{7 c _{1} e ^{x + 8}}{2} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d x} = 7 y e^{x + 8}

Solve separable ODE:

y = \frac{7 e ^{16 + 2 x}}{4} + \frac{7 c _{1} e ^{x + 8}}{2} + \frac{c _{1}^{2}}{4}

y = \frac{7 e ^{16 + 2 x}}{4} + \frac{7 c _{1} e ^{x + 8}}{2} + \frac{c _{1}^{2}}{4}

\int_{4}^{\infty} e^{- 5 x} d x

\frac{d y}{d x} = \frac{e ^{x}}{1 + e ^{x}}

y^{^{''}} + 8 y^{^{'}} + 17 y = 0, y (0) = 1, y^{^{'}} (0) = 0

\int \frac{( x + 2 ) ^{8}}{2 x} d x

e^{- 5}

What is the solution for (dy)/(dx)=sqrt(7y)e^{x+8} ?
The solution for (dy)/(dx)=sqrt(7y)e^{x+8} is y=(7e^{16+2x})/4+(sqrt(7)c_{1}e^{x+8})/2+(c_{1}^2)/4