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}}

\frac{d ^{2} y}{d x ^{2}} = 3 y

y^{^{''}} + 3 y^{^{'}} - 7 y = 0

y^{^{''}} + 1960 y = 0, y (0) = 0.015, y^{^{'}} (0) = 0

y^{^{''}} - 4 y + 7 y = 0

y^{^{''}} + 100 y = 0, y (π) = 5, y (0) = 2

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}