What is the solution for y^{''}-5y^'+6y=0,y(0)=2,y^'(0)=5 ?

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

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y^{''}-5y^'+6y=0,y(0)=2,y^'(0)=5

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y (0) = 2, y^{^{'}} (0) = 5

y = e^{3 t} + e^{2 t}

Solution steps

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

Solve linear ODE:

y = e^{3 t} + e^{2 t}

y = e^{3 t} + e^{2 t}

9 y^{^{''}} - 12 y^{^{'}} + 4 y = 0, y (0) = 4, y^{^{'}} (0) = - 1

y^{^{''}} - 25 y^{^{'}} + 144 y = 0

x^{^{''}} + 3 x^{^{'}} + x = 0

y^{^{''}} + 16 y^{^{'}} + 100 y = 0

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

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