What is the solution for (dy)/(dx)=sqrt(5y)e^{x+8} ?

The solution for (dy)/(dx)=sqrt(5y)e^{x+8} is y=(5e^{16+2x})/4+(sqrt(5)c_{1}e^{x+8})/2+(c_{1}^2)/4

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(dy)/(dx)=sqrt(5y)e^{x+8}

\frac{d y}{d x} = 5 y e^{x + 8}

y = \frac{5 e ^{16 + 2 x}}{4} + \frac{5 c _{1} e ^{x + 8}}{2} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d x} = 5 y e^{x + 8}

Solve separable ODE:

y = \frac{5 e ^{16 + 2 x}}{4} + \frac{5 c _{1} e ^{x + 8}}{2} + \frac{c _{1}^{2}}{4}

y = \frac{5 e ^{16 + 2 x}}{4} + \frac{5 c _{1} e ^{x + 8}}{2} + \frac{c _{1}^{2}}{4}

\int sec^{3} (7 x) d x

y^{^{'}} = sec (2) (x - y)

f (1) = 2 x^{4} - x^{3} + 6 x^{2}

x \to \infty lim (3 - x)

What is the solution for (dy)/(dx)=sqrt(5y)e^{x+8} ?
The solution for (dy)/(dx)=sqrt(5y)e^{x+8} is y=(5e^{16+2x})/4+(sqrt(5)c_{1}e^{x+8})/2+(c_{1}^2)/4