What is the solution for y^{''}-15y^'+54y=0,y(0)=9,y^'(0)=6 ?

The solution for y^{''}-15y^'+54y=0,y(0)=9,y^'(0)=6 is y=-16e^{9t}+25e^{6t}

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y^{''}-15y^'+54y=0,y(0)=9,y^'(0)=6

y^{^{''}} - 15 y^{^{'}} + 54 y = 0, y (0) = 9, y^{^{'}} (0) = 6

y = - 16 e^{9 t} + 25 e^{6 t}

Solution steps

y^{''} (t) - 15 y^{'} (t) + 54 y = 0

Solve linear ODE:

y = - 16 e^{9 t} + 25 e^{6 t}

y = - 16 e^{9 t} + 25 e^{6 t}

- x^{^{''}} + 2 x^{^{'}} + x = 0

\frac{d ^{4} y}{d x ^{4}} + 4 y = 0

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

y^{^{''}} - 3 y^{^{'}} - 40 y = 0

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = 2

What is the solution for y^{''}-15y^'+54y=0,y(0)=9,y^'(0)=6 ?
The solution for y^{''}-15y^'+54y=0,y(0)=9,y^'(0)=6 is y=-16e^{9t}+25e^{6t}