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

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

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(dy)/(dx)=sqrt(5y)e^{x+2}

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

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

Solution steps

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

Solve separable ODE:

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

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

f (x) = 2 x^{2} - 7

\int_{0}^{1} \frac{2 x}{( x ^{2} + 1 ) ^{2}} d x

x = \frac{1}{2} y^{2}, y = 1, y = - \frac{1}{2} x + 3

\frac{\partial}{\partial y} (\frac{- y}{y ^{2} + x ^{2}})

\frac{d}{d x} (\frac{3 x - 1}{x ^{2} + 2})

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