What is the solution for 16y^{''}-72y^'+81y=0,y(0)=8 ?

The solution for 16y^{''}-72y^'+81y=0,y(0)=8 is y=8e^{(9t)/4}+c_{2}e^{(9t)/4}t

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16y^{''}-72y^'+81y=0,y(0)=8

16 y^{^{''}} - 72 y^{^{'}} + 81 y = 0, y (0) = 8

y = 8 e^{\frac{9 t}{4}} + c_{2} e^{\frac{9 t}{4}} t

Solution steps

16 y^{''} (t) - 72 y^{'} (t) + 81 y = 0

Solve linear ODE:

y = 8 e^{\frac{9 t}{4}} + c_{2} e^{\frac{9 t}{4}} t

y = 8 e^{\frac{9 t}{4}} + c_{2} e^{\frac{9 t}{4}} t

y^{^{'''}} - 2 y^{^{''}} - 40 y^{^{'}} - 64 y = 0

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 29 y = 0

x^{^{''}} + 2 x^{^{'}} + 26 x = 0

\frac{d ^{2} f}{d x ^{2}} + k^{2} f (x) = 0

2 y^{^{''}} + 3 y^{^{'}} = 0, y (0) = 1, y^{^{'}} (0) = 1

What is the solution for 16y^{''}-72y^'+81y=0,y(0)=8 ?
The solution for 16y^{''}-72y^'+81y=0,y(0)=8 is y=8e^{(9t)/4}+c_{2}e^{(9t)/4}t