What is the solution for x^2(dy)/(dx)+8x(dy)/(dx)+6y=0 ?

The solution for x^2(dy)/(dx)+8x(dy)/(dx)+6y=0 is y=e^{-6(1/8 ln(x)-1/8 ln(x+8))+c_{1}}

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x^2(dy)/(dx)+8x(dy)/(dx)+6y=0

x^{2} \frac{d y}{d x} + 8 x \frac{d y}{d x} + 6 y = 0

y = e^{- 6 (\frac{1}{8} l n (x) - \frac{1}{8} l n (x + 8)) + c_{1}}

Solution steps

x^{2} \frac{d y}{d x} + 8 x \frac{d y}{d x} + 6 y = 0

Solve separable ODE:

y = e^{- 6 (\frac{1}{8} l n (x) - \frac{1}{8} l n (x + 8)) + c_{1}}

y = e^{- 6 (\frac{1}{8} l n (x) - \frac{1}{8} l n (x + 8)) + c_{1}}

\frac{d y}{d x} = \frac{y cos ( x )}{1 + 2 y ^{2}}, y (0) = 1

x^{^{'}} = - 5 x

\frac{d y}{d x} - \frac{y}{1 - x ^{2}} = 0

\frac{d y}{d x} = 5 x sec (y)

3 x (y^{2} + 1) d x + y (x^{2} + 1) d y = 0

What is the solution for x^2(dy)/(dx)+8x(dy)/(dx)+6y=0 ?
The solution for x^2(dy)/(dx)+8x(dy)/(dx)+6y=0 is y=e^{-6(1/8 ln(x)-1/8 ln(x+8))+c_{1}}