What is the solution for 6y^{''}-5y^'+y=0,y(0)=e^{x/2} ?

The solution for 6y^{''}-5y^'+y=0,y(0)=e^{x/2} is y=c_{1}e^{x/2}+c_{2}e^{x/3}

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6y^{''}-5y^'+y=0,y(0)=e^{x/2}

6 y^{^{''}} - 5 y^{^{'}} + y = 0, y (0) = e^{\frac{x}{2}}

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{3}}

Solution steps

6 y^{''} (x) - 5 y^{'} (x) + y = 0

Solve linear ODE:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{3}}

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{3}}

y^{^{'''}} + 25 y^{^{'}} = 0

y^{^{'''}} + 2 y^{^{''}} - 20 y^{^{'}} + 24 y = 0

0.25 y^{^{''}} + 10 y^{^{'}} + 1000 y = 0

y^{^{'''}} + y^{^{'}} = 0, y (0) = 1, y^{^{''}} (0) = 2

y^{^{''}} - 8 y^{^{''}} + 16 y = 0

What is the solution for 6y^{''}-5y^'+y=0,y(0)=e^{x/2} ?
The solution for 6y^{''}-5y^'+y=0,y(0)=e^{x/2} is y=c_{1}e^{x/2}+c_{2}e^{x/3}