What is the solution for y^{'''}-11y^{''}+51y^'-41y=0 ?

The solution for y^{'''}-11y^{''}+51y^'-41y=0 is y=c_{1}e^t+e^{5t}(c_{2}cos(4t)+c_{3}sin(4t))

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y^{'''}-11y^{''}+51y^'-41y=0

y^{^{'''}} - 11 y^{^{''}} + 51 y^{^{'}} - 41 y = 0

y = c_{1} e^{t} + e^{5 t} (c_{2} cos (4 t) + c_{3} sin (4 t))

Solution steps

y^{'''} (t) - 11 y^{''} (t) + 51 y^{'} (t) - 41 y = 0

Solve linear ODE:

y = c_{1} e^{t} + e^{5 t} (c_{2} cos (4 t) + c_{3} sin (4 t))

y = c_{1} e^{t} + e^{5 t} (c_{2} cos (4 t) + c_{3} sin (4 t))

x y^{^{'}} - 2 y = - x

\frac{x + 1}{x}

\frac{10}{( 5 s + 1 ) ( s + 2 ) ^{2}}

4 - t^{2}

x \to 2 - lim (3 x^{2} - 12)

What is the solution for y^{'''}-11y^{''}+51y^'-41y=0 ?
The solution for y^{'''}-11y^{''}+51y^'-41y=0 is y=c_{1}e^t+e^{5t}(c_{2}cos(4t)+c_{3}sin(4t))