What is the solution for y^{''}-7y^'+12y=0,y(0)=10,y^'(0)=27 ?

The solution for y^{''}-7y^'+12y=0,y(0)=10,y^'(0)=27 is y=-3e^{4t}+13e^{3t}

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y^{''}-7y^'+12y=0,y(0)=10,y^'(0)=27

y^{^{''}} - 7 y^{^{'}} + 12 y = 0, y (0) = 10, y^{^{'}} (0) = 27

y = - 3 e^{4 t} + 13 e^{3 t}

Solution steps

y^{''} (t) - 7 y^{'} (t) + 12 y = 0

Solve linear ODE:

y = - 3 e^{4 t} + 13 e^{3 t}

y = - 3 e^{4 t} + 13 e^{3 t}

y^{^{''}} + 5 y^{^{'}} + 4 y = 0, y (0) = 7, y^{^{'}} (0) = - 13

y^{^{'''}} - 3 y^{^{''}} + 5 y^{^{'}} + 9 y = 0

3 y^{^{''}} + 2 y^{^{'}} + y = 0

\frac{x ^{^{''}} - 3 x ^{^{'}}}{2} = 2 x - \frac{( x ^{^{'}} - 3 x )}{2}

y^{^{''}} + y^{^{'}} - 12 y = 0, y (0) = - 6, y^{^{'}} (0) = 17

What is the solution for y^{''}-7y^'+12y=0,y(0)=10,y^'(0)=27 ?
The solution for y^{''}-7y^'+12y=0,y(0)=10,y^'(0)=27 is y=-3e^{4t}+13e^{3t}