What is the solution for (dy)/(dx)=sqrt(9y)e^{x+5} ?

The solution for (dy)/(dx)=sqrt(9y)e^{x+5} is y=(9e^{10+2x})/4+(3c_{1}e^{x+5})/2+(c_{1}^2)/4

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(dy)/(dx)=sqrt(9y)e^{x+5}

\frac{d y}{d x} = 9 y e^{x + 5}

y = \frac{9 e ^{10 + 2 x}}{4} + \frac{3 c _{1} e ^{x + 5}}{2} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d x} = 9 y e^{x + 5}

Solve separable ODE:

y = \frac{9 e ^{10 + 2 x}}{4} + \frac{3 c _{1} e ^{x + 5}}{2} + \frac{c _{1}^{2}}{4}

y = \frac{9 e ^{10 + 2 x}}{4} + \frac{3 c _{1} e ^{x + 5}}{2} + \frac{c _{1}^{2}}{4}

y^{^{'}} = x sin (2 y)

\int_{2}^{5} e^{2 x} d x

\frac{\partial}{\partial x} (4 x^{5} - 2 y^{- 3})

\frac{9 + 2 x - 6 x}{x}

y^{^{''}} + y^{^{'}} - 2 y = 0

What is the solution for (dy)/(dx)=sqrt(9y)e^{x+5} ?
The solution for (dy)/(dx)=sqrt(9y)e^{x+5} is y=(9e^{10+2x})/4+(3c_{1}e^{x+5})/2+(c_{1}^2)/4