What is the solution for y^'-5y^{(2)}e^{(-3x)}=0,y(0)=9 ?

The solution for y^'-5y^{(2)}e^{(-3x)}=0,y(0)=9 is y=-(9e^{3x})/(-15+14e^{3x)}

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y^'-5y^{(2)}e^{(-3x)}=0,y(0)=9

y^{^{'}} - 5 y^{(2)} e^{(- 3 x)} = 0, y (0) = 9

y = - \frac{9 e ^{3 x}}{- 15 + 14 e ^{3 x}}

Solution steps

y^{'} (x) - 5 y^{(2)} e^{(- 3 x)} = 0

Solve separable ODE:

y = - \frac{9 e ^{3 x}}{- 15 + 14 e ^{3 x}}

y = - \frac{9 e ^{3 x}}{- 15 + 14 e ^{3 x}}

\int \frac{x ^{3}}{x ^{2} + 2 x + 1} d x

y = \frac{( x ^{2} )}{8 + x}

\int a e^{- m x} d x

\frac{d y}{d x} + (\frac{3}{x}) y = - 2 x + 7

What is the solution for y^'-5y^{(2)}e^{(-3x)}=0,y(0)=9 ?
The solution for y^'-5y^{(2)}e^{(-3x)}=0,y(0)=9 is y=-(9e^{3x})/(-15+14e^{3x)}