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

解

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}

解答ステップ

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

線形 ODE を解く:

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}