What is the solution for (dy)/(dx)=sqrt(5y)*e^{x+6} ?

The solution for (dy)/(dx)=sqrt(5y)*e^{x+6} is y=(5e^{12+2x})/4+(sqrt(5)c_{1}e^{x+6})/2+(c_{1}^2)/4

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(dy)/(dx)=sqrt(5y)*e^{x+6}

\frac{d y}{d x} = 5 y \cdot e^{x + 6}

y = \frac{5 e ^{12 + 2 x}}{4} + \frac{5 c _{1} e ^{x + 6}}{2} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d x} = 5 y \cdot e^{x + 6}

Solve separable ODE:

y = \frac{5 e ^{12 + 2 x}}{4} + \frac{5 c _{1} e ^{x + 6}}{2} + \frac{c _{1}^{2}}{4}

y = \frac{5 e ^{12 + 2 x}}{4} + \frac{5 c _{1} e ^{x + 6}}{2} + \frac{c _{1}^{2}}{4}

What is the solution for (dy)/(dx)=sqrt(5y)*e^{x+6} ?
The solution for (dy)/(dx)=sqrt(5y)*e^{x+6} is y=(5e^{12+2x})/4+(sqrt(5)c_{1}e^{x+6})/2+(c_{1}^2)/4