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

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

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

x^{3} y^{^{'''}} + 3 x^{2} y^{^{''}} - 2 x y^{^{'}} + 2 y = 0

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

Solution steps

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

Solve linear ODE:

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

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

x \to 5 lim (\frac{6}{x - 5})

\int \frac{sin ( x )}{( cos ( x ) ) ^{3}} d x

\frac{\partial}{\partial x} (\frac{x ^{4} + y ^{2}}{x y})

\int 9 x + 5 d x

x \to - 6 + lim (\frac{- 2 x}{x + 6})

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