What is the solution for y^{''}-6y^'+113y=0 ?

The solution for y^{''}-6y^'+113y=0 is y=e^{3t}(c_{1}cos(2sqrt(26)t)+c_{2}sin(2sqrt(26)t))

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y^{''}-6y^'+113y=0

y^{^{''}} - 6 y^{^{'}} + 113 y = 0

y = e^{3 t} (c_{1} cos (226 t) + c_{2} sin (226 t))

Solution steps

y^{''} (t) - 6 y^{'} (t) + 113 y = 0

Solve linear ODE:

y = e^{3 t} (c_{1} cos (226 t) + c_{2} sin (226 t))

y = e^{3 t} (c_{1} cos (226 t) + c_{2} sin (226 t))

10 \frac{d ^{2} y}{d x ^{2}} + 20 \frac{d y}{d x} + 10 y = 0

y^{^{''}} + 4 y^{^{'}} + 3 y = 0, y (0) = 6, y^{^{'}} (0) = 2

x^{^{''}} + 5 x^{^{'}} = 0

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

\frac{d ^{2} y}{d x ^{2}} + 49 y = 0

What is the solution for y^{''}-6y^'+113y=0 ?
The solution for y^{''}-6y^'+113y=0 is y=e^{3t}(c_{1}cos(2sqrt(26)t)+c_{2}sin(2sqrt(26)t))