What is the solution for 6y^{''}-5y^'+y=0,y(0)=-1,y^'(0)=1 ?

The solution for 6y^{''}-5y^'+y=0,y(0)=-1,y^'(0)=1 is y=8e^{t/2}-9e^{t/3}

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6y^{''}-5y^'+y=0,y(0)=-1,y^'(0)=1

6 y^{^{''}} - 5 y^{^{'}} + y = 0, y (0) = - 1, y^{^{'}} (0) = 1

y = 8 e^{\frac{t}{2}} - 9 e^{\frac{t}{3}}

Solution steps

6 y^{''} (t) - 5 y^{'} (t) + y = 0

Solve linear ODE:

y = 8 e^{\frac{t}{2}} - 9 e^{\frac{t}{3}}

y = 8 e^{\frac{t}{2}} - 9 e^{\frac{t}{3}}

(D^{2} + 9 D + 18) y = 0

y^{^{'''}} - y^{^{''}} - 5 y^{^{'}} - 3 y = 0

x^{^{''}} + 10 x^{^{'}} + 16 x = 0

y^{^{''}} - 4 y^{^{'}} + 8 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 5 y^{^{'}} + 10 y = 0

What is the solution for 6y^{''}-5y^'+y=0,y(0)=-1,y^'(0)=1 ?
The solution for 6y^{''}-5y^'+y=0,y(0)=-1,y^'(0)=1 is y=8e^{t/2}-9e^{t/3}