What is the solution for x^3y^{'''}+6x^2y^{''}+7xy^'+y=0 ?

The solution for x^3y^{'''}+6x^2y^{''}+7xy^'+y=0 is y=(c_{1})/x+(c_{2}ln(x))/x+(c_{3}ln^2(x))/x

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x^3y^{'''}+6x^2y^{''}+7xy^'+y=0

x^{3} y^{^{'''}} + 6 x^{2} y^{^{''}} + 7 x y^{^{'}} + y = 0

y = \frac{c _{1}}{x} + \frac{c _{2} ln ( x )}{x} + \frac{c _{3} ln ^{2} ( x )}{x}

Solution steps

x^{3} y^{'''} (x) + 6 x^{2} y^{''} (x) + 7 x y^{'} (x) + y = 0

Solve linear ODE:

y = \frac{c _{1}}{x} + \frac{c _{2} ln ( x )}{x} + \frac{c _{3} ln ^{2} ( x )}{x}

y = \frac{c _{1}}{x} + \frac{c _{2} ln ( x )}{x} + \frac{c _{3} ln ^{2} ( x )}{x}

\frac{cos ( x )}{1 - sin ( x )}

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

f (x) = sec (4 x)

\int x \cdot ln (x^{6}) d x

x \to \infty lim (9 + \frac{8}{x})

What is the solution for x^3y^{'''}+6x^2y^{''}+7xy^'+y=0 ?
The solution for x^3y^{'''}+6x^2y^{''}+7xy^'+y=0 is y=(c_{1})/x+(c_{2}ln(x))/x+(c_{3}ln^2(x))/x