What is the solution for (D^4-6D^3+5D^2)y=0 ?

The solution for (D^4-6D^3+5D^2)y=0 is y=c_{1}e^x+c_{2}e^{5x}+c_{3}+c_{4}x

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(D^4-6D^3+5D^2)y=0

(D^{4} - 6 D^{3} + 5 D^{2}) y = 0

y = c_{1} e^{x} + c_{2} e^{5 x} + c_{3} + c_{4} x

Solution steps

(D^{4} - 6 D^{3} + 5 D^{2}) y = 0

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{5 x} + c_{3} + c_{4} x

y = c_{1} e^{x} + c_{2} e^{5 x} + c_{3} + c_{4} x

y^{^{'''}} - 24 y^{^{''}} + 192 y^{^{'}} - 512 y = 0

y^{^{''}} + 4 \cdot π \cdot \frac{y ^{^{'}}}{20} + 100 \cdot π^{2} \cdot y = 0

(d^{6} - 4 d^{4} + 4 d^{2}) \cdot y = 0

4 y^{^{'''}} - 12 y^{^{'}} + 9 y^{^{'}} = 0

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

What is the solution for (D^4-6D^3+5D^2)y=0 ?
The solution for (D^4-6D^3+5D^2)y=0 is y=c_{1}e^x+c_{2}e^{5x}+c_{3}+c_{4}x