What is the solution for (2+x)y^'=9y ?

The solution for (2+x)y^'=9y is

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(2+x)y^'=9y

(2 + x) y^{^{'}} = 9 y

y = 512 e^{c_{1}} + 2304 e^{c_{1}} x + 4608 e^{c_{1}} x^{2} + 5376 e^{c_{1}} x^{3} + 4032 e^{c_{1}} x^{4} + 2016 e^{c_{1}} x^{5} + 672 e^{c_{1}} x^{6} + 144 e^{c_{1}} x^{7} + 18 e^{c_{1}} x^{8} + e^{c_{1}} x^{9}

Solution steps

(2 + x) y^{'} (x) = 9 y

Solve separable ODE:

y = 512 e^{c_{1}} + 2304 e^{c_{1}} x + 4608 e^{c_{1}} x^{2} + 5376 e^{c_{1}} x^{3} + 4032 e^{c_{1}} x^{4} + 2016 e^{c_{1}} x^{5} + 672 e^{c_{1}} x^{6} + 144 e^{c_{1}} x^{7} + 18 e^{c_{1}} x^{8} + e^{c_{1}} x^{9}

y = 512 e^{c_{1}} + 2304 e^{c_{1}} x + 4608 e^{c_{1}} x^{2} + 5376 e^{c_{1}} x^{3} + 4032 e^{c_{1}} x^{4} + 2016 e^{c_{1}} x^{5} + 672 e^{c_{1}} x^{6} + 144 e^{c_{1}} x^{7} + 18 e^{c_{1}} x^{8} + e^{c_{1}} x^{9}

f (x) = 3 x + 55, at x = 3

x \to + 2 lim (\frac{g ( x )}{h ( x )})

\int tan^{2} (x) sec^{2} (x) sin (x) d x

y = \frac{( x ^{9} )}{f ( x )}

\frac{\partial}{\partial x} (x e^{2 x} cos (3 x))