What is the solution for (dy)/(dx)=sqrt(9y)e^{x+3} ?

The solution for (dy)/(dx)=sqrt(9y)e^{x+3} is y=(9e^{6+2x})/4+(3c_{1}e^{x+3})/2+(c_{1}^2)/4

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(dy)/(dx)=sqrt(9y)e^{x+3}

\frac{d y}{d x} = 9 y e^{x + 3}

y = \frac{9 e ^{6 + 2 x}}{4} + \frac{3 c _{1} e ^{x + 3}}{2} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d x} = 9 y e^{x + 3}

Solve separable ODE:

y = \frac{9 e ^{6 + 2 x}}{4} + \frac{3 c _{1} e ^{x + 3}}{2} + \frac{c _{1}^{2}}{4}

y = \frac{9 e ^{6 + 2 x}}{4} + \frac{3 c _{1} e ^{x + 3}}{2} + \frac{c _{1}^{2}}{4}

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\frac{d}{d x} (- \frac{x}{4} + \frac{3}{4})

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(- \frac{1}{4 x ^{\frac{3}{2}}})^{^{'}}

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What is the solution for (dy)/(dx)=sqrt(9y)e^{x+3} ?
The solution for (dy)/(dx)=sqrt(9y)e^{x+3} is y=(9e^{6+2x})/4+(3c_{1}e^{x+3})/2+(c_{1}^2)/4