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

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

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(dy)/(dx)=sqrt(7y)e^{x+2}

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

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

Solution steps

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

Solve separable ODE:

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

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

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

x \to - 5 + lim (\frac{- 1}{x ^{2} - 25})

\frac{d}{d x} (g (x) \cdot (a x^{2} + x))

n = 2 \sum \infty \frac{( 3 ^{3 n} )}{2 ^{2 n - 2}}

x \to 10 lim (\frac{x}{x ^{2} - 100})

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