What is the solution for y^{''}-5y^'+6y=0,y(1)=7 ?

The solution for y^{''}-5y^'+6y=0,y(1)=7 is y=e^{3t-3}(7-e^2c_{2})+c_{2}e^{2t}

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y^{''}-5y^'+6y=0,y(1)=7

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y (1) = 7

y = e^{3 t - 3} (7 - e^{2} c_{2}) + c_{2} e^{2 t}

Solution steps

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

Solve linear ODE:

y = e^{3 t - 3} (7 - e^{2} c_{2}) + c_{2} e^{2 t}

y = e^{3 t - 3} (7 - e^{2} c_{2}) + c_{2} e^{2 t}

y^{^{''}} - 4 y^{^{'}} + 5 y = 0, y (0) = 1, y^{^{'}} (0) = 6

y^{^{''}} - 12 y^{^{'}} + 36 y = 0, y (- 1) = 2, y^{^{'}} (- 1) = 5

4 y^{^{''}} - 24 y^{^{'}} + 37 y = 0, y (0) = - 9

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

8 y^{^{''}} + 16 y^{^{'}} + 128 y = 0, y (0) = 5, y^{^{'}} (0) = 8

What is the solution for y^{''}-5y^'+6y=0,y(1)=7 ?
The solution for y^{''}-5y^'+6y=0,y(1)=7 is y=e^{3t-3}(7-e^2c_{2})+c_{2}e^{2t}