What is the solution for 36y^{''}-84y^'+49y=0 ?

The solution for 36y^{''}-84y^'+49y=0 is y=c_{1}e^{(7t)/6}+c_{2}e^{(7t)/6}t

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36y^{''}-84y^'+49y=0

36 y^{^{''}} - 84 y^{^{'}} + 49 y = 0

y = c_{1} e^{\frac{7 t}{6}} + c_{2} e^{\frac{7 t}{6}} t

Solution steps

36 y^{''} (t) - 84 y^{'} (t) + 49 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{7 t}{6}} + c_{2} e^{\frac{7 t}{6}} t

y = c_{1} e^{\frac{7 t}{6}} + c_{2} e^{\frac{7 t}{6}} t

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

20 y^{^{''}} + 200 y^{^{'}} + 520 y = 0

y^{^{''}} - 6 y^{^{'}} + 9 y = 0

- a y^{^{''}} = - k y

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = 1

What is the solution for 36y^{''}-84y^'+49y=0 ?
The solution for 36y^{''}-84y^'+49y=0 is y=c_{1}e^{(7t)/6}+c_{2}e^{(7t)/6}t