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

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

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(dy)/(dx)=sqrt(4y)e^{x+7}

\frac{d y}{d x} = 4 y e^{x + 7}

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

Solution steps

\frac{d y}{d x} = 4 y e^{x + 7}

Solve separable ODE:

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

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

\int (x + 3) (x^{2} + 6 x - 7)^{6} d x

y^{^{'}} = y (x y^{5} + 4)

(x^{3} + 7)^{\frac{2}{3}}

f (x) = - 3 x^{2} - 3 x + 2, at x = 1

f (x) = 3 x^{2} + e^{2 x} + π^{2}

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