What is the solution for y^{''''}-7y^{'''}+12y^{''}=0 ?

The solution for y^{''''}-7y^{'''}+12y^{''}=0 is y=c_{1}e^{3t}+c_{2}e^{4t}+c_{3}+c_{4}t

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y^{''''}-7y^{'''}+12y^{''}=0

y^{^{''''}} - 7 y^{^{'''}} + 12 y^{^{''}} = 0

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

Solution steps

y^{(4)} (t) - 7 y^{'''} (t) + 12 y^{''} (t) = 0

Solve linear ODE:

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

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

y^{^{''}} + 6 y^{^{''}} + 11 y^{^{'}} + 6 y = 0

y^{^{'''}} + 3 y^{^{''}} - 54 y^{^{'}} = 0

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

5 y^{^{''}} - 6 y^{^{'}} + y = 0, y (0) = 5, y^{^{'}} (0) = \frac{1}{5}

x^{^{''}} + 4 x^{^{'}} + 8 x = 0

What is the solution for y^{''''}-7y^{'''}+12y^{''}=0 ?
The solution for y^{''''}-7y^{'''}+12y^{''}=0 is y=c_{1}e^{3t}+c_{2}e^{4t}+c_{3}+c_{4}t