What is the solution for (dy)/(dx)=sqrt(3y)e^{x+7} ?

The solution for (dy)/(dx)=sqrt(3y)e^{x+7} is y=(3e^{14+2x})/4+(sqrt(3)c_{1}e^{x+7})/2+(c_{1}^2)/4

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(dy)/(dx)=sqrt(3y)e^{x+7}

\frac{d y}{d x} = 3 y e^{x + 7}

y = \frac{3 e ^{14 + 2 x}}{4} + \frac{3 c _{1} e ^{x + 7}}{2} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d x} = 3 y e^{x + 7}

Solve separable ODE:

y = \frac{3 e ^{14 + 2 x}}{4} + \frac{3 c _{1} e ^{x + 7}}{2} + \frac{c _{1}^{2}}{4}

y = \frac{3 e ^{14 + 2 x}}{4} + \frac{3 c _{1} e ^{x + 7}}{2} + \frac{c _{1}^{2}}{4}

\int - \frac{cos ( x )}{x} d x

y^{^{''}} - 4 y^{^{'}} + 5 y = e^{- x}

y = x^{2} - 15, y = 1

(x, y) \to (0, 1) lim (\frac{e ^{x y}}{x + 1})

\int cos (y^{3}) d y

What is the solution for (dy)/(dx)=sqrt(3y)e^{x+7} ?
The solution for (dy)/(dx)=sqrt(3y)e^{x+7} is y=(3e^{14+2x})/4+(sqrt(3)c_{1}e^{x+7})/2+(c_{1}^2)/4