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

The solution for x^3y^{'''}-6y=0 is y=c_{1}x^3+c_{2}cos(sqrt(2)ln(x))+c_{3}sin(sqrt(2)ln(x))

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

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

y = c_{1} x^{3} + c_{2} cos (2 ln (x)) + c_{3} sin (2 ln (x))

Solution steps

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

Solve linear ODE:

y = c_{1} x^{3} + c_{2} cos (2 ln (x)) + c_{3} sin (2 ln (x))

y = c_{1} x^{3} + c_{2} cos (2 ln (x)) + c_{3} sin (2 ln (x))

What is the solution for x^3y^{'''}-6y=0 ?
The solution for x^3y^{'''}-6y=0 is y=c_{1}x^3+c_{2}cos(sqrt(2)ln(x))+c_{3}sin(sqrt(2)ln(x))