What is the solution for 49y^{''}-112y^'+64y=0 ?

The solution for 49y^{''}-112y^'+64y=0 is y=c_{1}e^{(8t)/7}+c_{2}e^{(8t)/7}t

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49y^{''}-112y^'+64y=0

49 y^{^{''}} - 112 y^{^{'}} + 64 y = 0

y = c_{1} e^{\frac{8 t}{7}} + c_{2} e^{\frac{8 t}{7}} t

Solution steps

49 y^{''} (t) - 112 y^{'} (t) + 64 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{8 t}{7}} + c_{2} e^{\frac{8 t}{7}} t

y = c_{1} e^{\frac{8 t}{7}} + c_{2} e^{\frac{8 t}{7}} t

- \frac{d ^{2} y}{d x ^{2}} + 400 y = 0

y^{^{''}} + 4 y - 5 y = 0

y^{^{''}} - 2 y = 0, y (0) = 1, y^{^{'}} (0) = 6

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = - 1, y^{^{'}} (0) = - \frac{9}{4}

y^{^{''}} + 25 y = 0, y^{^{'}} (π) = 0, y^{^{'}} (0) = 0

What is the solution for 49y^{''}-112y^'+64y=0 ?
The solution for 49y^{''}-112y^'+64y=0 is y=c_{1}e^{(8t)/7}+c_{2}e^{(8t)/7}t