What is the solution for y^{'''}-11y^{''}+28y^'=0 ?

The solution for y^{'''}-11y^{''}+28y^'=0 is y=c_{1}+c_{2}e^{4t}+c_{3}e^{7t}

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y^{'''}-11y^{''}+28y^'=0

y^{^{'''}} - 11 y^{^{''}} + 28 y^{^{'}} = 0

y = c_{1} + c_{2} e^{4 t} + c_{3} e^{7 t}

Solution steps

y^{'''} (t) - 11 y^{''} (t) + 28 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{4 t} + c_{3} e^{7 t}

y = c_{1} + c_{2} e^{4 t} + c_{3} e^{7 t}

(d^{4} + 2 d^{2} + 1) y = 0

\frac{d ^{3} y}{d x ^{3}} - \frac{d ^{2} y}{d x ^{2}} = 0

y^{^{'''}} - y^{^{''}} + 25 y^{^{'}} - 25 y = 0

y^{^{''}} - 16 y^{^{'}} - 63 y = 0

y^{^{''}} + \frac{3}{2} y^{^{'}} + \frac{3}{8} y = 0

What is the solution for y^{'''}-11y^{''}+28y^'=0 ?
The solution for y^{'''}-11y^{''}+28y^'=0 is y=c_{1}+c_{2}e^{4t}+c_{3}e^{7t}