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

The solution for (dy)/(dx)=sqrt(7y)e^{x+3} is y=(7e^{6+2x})/4+(sqrt(7)c_{1}e^{x+3})/2+(c_{1}^2)/4

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

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

y = \frac{7 e ^{6 + 2 x}}{4} + \frac{7 c _{1} e ^{x + 3}}{2} + \frac{c _{1}^{2}}{4}

Solution steps

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

Solve separable ODE:

y = \frac{7 e ^{6 + 2 x}}{4} + \frac{7 c _{1} e ^{x + 3}}{2} + \frac{c _{1}^{2}}{4}

y = \frac{7 e ^{6 + 2 x}}{4} + \frac{7 c _{1} e ^{x + 3}}{2} + \frac{c _{1}^{2}}{4}

\frac{d}{d x} ((2^{x})^{8})

\frac{d}{d x} (x^{2} + e^{x})

x \to 1 lim (\frac{x + 3}{2})

\frac{\partial}{\partial x} (3 x^{2} - 2 y^{3})

\frac{d ^{2}}{d x ^{2}} (cos (x^{2}))

What is the solution for (dy)/(dx)=sqrt(7y)e^{x+3} ?
The solution for (dy)/(dx)=sqrt(7y)e^{x+3} is y=(7e^{6+2x})/4+(sqrt(7)c_{1}e^{x+3})/2+(c_{1}^2)/4