What is the solution for 3xy^{''}-2xy^'+11xy=0 ?

The solution for 3xy^{''}-2xy^'+11xy=0 is y=e^{x/3}(c_{1}cos((4sqrt(2)x)/3)+c_{2}sin((4sqrt(2)x)/3))

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3xy^{''}-2xy^'+11xy=0

3 x y^{^{''}} - 2 x y^{^{'}} + 11 x y = 0

y = e^{\frac{x}{3}} (c_{1} cos (\frac{4 2 x}{3}) + c_{2} sin (\frac{4 2 x}{3}))

Solution steps

3 x y^{''} (x) - 2 x y^{'} (x) + 11 x y = 0

Solve linear ODE:

y = e^{\frac{x}{3}} (c_{1} cos (\frac{4 2 x}{3}) + c_{2} sin (\frac{4 2 x}{3}))

y = e^{\frac{x}{3}} (c_{1} cos (\frac{4 2 x}{3}) + c_{2} sin (\frac{4 2 x}{3}))

What is the solution for 3xy^{''}-2xy^'+11xy=0 ?
The solution for 3xy^{''}-2xy^'+11xy=0 is y=e^{x/3}(c_{1}cos((4sqrt(2)x)/3)+c_{2}sin((4sqrt(2)x)/3))