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}}

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}