What is the solution for 6y^{''}+(-5)y^'+y=0,y(0)=4,y^'(0)=0 ?

The solution for 6y^{''}+(-5)y^'+y=0,y(0)=4,y^'(0)=0 is y=-8e^{t/2}+12e^{t/3}

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6y^{''}+(-5)y^'+y=0,y(0)=4,y^'(0)=0

6 y^{^{''}} + (- 5) y^{^{'}} + y = 0, y (0) = 4, y^{^{'}} (0) = 0

y = - 8 e^{\frac{t}{2}} + 12 e^{\frac{t}{3}}

Solution steps

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

Solve linear ODE:

y = - 8 e^{\frac{t}{2}} + 12 e^{\frac{t}{3}}

y = - 8 e^{\frac{t}{2}} + 12 e^{\frac{t}{3}}

What is the solution for 6y^{''}+(-5)y^'+y=0,y(0)=4,y^'(0)=0 ?
The solution for 6y^{''}+(-5)y^'+y=0,y(0)=4,y^'(0)=0 is y=-8e^{t/2}+12e^{t/3}