What is the solution for (2+x)y^'=8y ?

The solution for (2+x)y^'=8y is

Popular >

(2+x)y^'=8y

(2 + x) y^{^{'}} = 8 y

y = 256 e^{c_{1}} + 1024 e^{c_{1}} x + 1792 e^{c_{1}} x^{2} + 1792 e^{c_{1}} x^{3} + 1120 e^{c_{1}} x^{4} + 448 e^{c_{1}} x^{5} + 112 e^{c_{1}} x^{6} + 16 e^{c_{1}} x^{7} + e^{c_{1}} x^{8}

Solution steps

(2 + x) y^{'} (x) = 8 y

Solve separable ODE:

y = 256 e^{c_{1}} + 1024 e^{c_{1}} x + 1792 e^{c_{1}} x^{2} + 1792 e^{c_{1}} x^{3} + 1120 e^{c_{1}} x^{4} + 448 e^{c_{1}} x^{5} + 112 e^{c_{1}} x^{6} + 16 e^{c_{1}} x^{7} + e^{c_{1}} x^{8}

y = 256 e^{c_{1}} + 1024 e^{c_{1}} x + 1792 e^{c_{1}} x^{2} + 1792 e^{c_{1}} x^{3} + 1120 e^{c_{1}} x^{4} + 448 e^{c_{1}} x^{5} + 112 e^{c_{1}} x^{6} + 16 e^{c_{1}} x^{7} + e^{c_{1}} x^{8}

x \to 0 lim (e^{x} - e^{- x})

\frac{d y}{d x} = 9 e^{x - y}

f (x) = 3 x^{3} (x^{2} - 3 x + 5)

\frac{d}{d x} (sin (3 x) + cos (4 x))