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

The solution for x^3y^{'''}-3x^2y^{''}+6xy^'-6y=0 is y=c_{1}x+c_{2}x^2+c_{3}x^3

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

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

y = c_{1} x + c_{2} x^{2} + c_{3} x^{3}

Solution steps

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

Solve linear ODE:

y = c_{1} x + c_{2} x^{2} + c_{3} x^{3}

y = c_{1} x + c_{2} x^{2} + c_{3} x^{3}

What is the solution for x^3y^{'''}-3x^2y^{''}+6xy^'-6y=0 ?
The solution for x^3y^{'''}-3x^2y^{''}+6xy^'-6y=0 is y=c_{1}x+c_{2}x^2+c_{3}x^3