What is the solution for 2y^{''}-11y^'+5y=0,y(0)=13,y^'(0)=47 ?

The solution for 2y^{''}-11y^'+5y=0,y(0)=13,y^'(0)=47 is y=9e^{5t}+4e^{t/2}

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2y^{''}-11y^'+5y=0,y(0)=13,y^'(0)=47

2 y^{^{''}} - 11 y^{^{'}} + 5 y = 0, y (0) = 13, y^{^{'}} (0) = 47

y = 9 e^{5 t} + 4 e^{\frac{t}{2}}

Solution steps

2 y^{''} (t) - 11 y^{'} (t) + 5 y = 0

Solve linear ODE:

y = 9 e^{5 t} + 4 e^{\frac{t}{2}}

y = 9 e^{5 t} + 4 e^{\frac{t}{2}}

y^{^{'''}} + 36 y^{^{'}} = 0

9 y^{^{''}} - 48 y^{^{'}} + 64 y = 0

y^{^{''}} + 7 y^{^{'}} + 10 y = 0, y (0) = 1, y^{^{'}} (0) = 1

755 x^{^{''}} + 2 x^{^{'}} + 10 x = 0

(D^{(6)} - 4 D^{(4)} + 4 D^{(2)}) y = 0

What is the solution for 2y^{''}-11y^'+5y=0,y(0)=13,y^'(0)=47 ?
The solution for 2y^{''}-11y^'+5y=0,y(0)=13,y^'(0)=47 is y=9e^{5t}+4e^{t/2}