What is the solution for y^{''}-8y^'+16y=0,y(0)=4,y(1)=5 ?

The solution for y^{''}-8y^'+16y=0,y(0)=4,y(1)=5 is y=4e^{4t}+(5-4e^4)e^{4t-4}t

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y^{''}-8y^'+16y=0,y(0)=4,y(1)=5

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 4, y (1) = 5

y = 4 e^{4 t} + (5 - 4 e^{4}) e^{4 t - 4} t

Solution steps

y^{''} (t) - 8 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = 4 e^{4 t} + (5 - 4 e^{4}) e^{4 t - 4} t

y = 4 e^{4 t} + (5 - 4 e^{4}) e^{4 t - 4} t

0.05 y^{^{''}} + 2 y^{^{'}} + 100 y = 0

x^{^{''}} + \frac{0}{\frac{1}{32}} x^{^{'}} + \frac{13}{\frac{1}{32}} x = 0

y^{^{''}} + 4 y^{^{'}} + 20 y = 0, y (π) = 5, y (0) = 6

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

1.5 y^{^{''}} + 12 y^{^{'}} + 24 y = 0

What is the solution for y^{''}-8y^'+16y=0,y(0)=4,y(1)=5 ?
The solution for y^{''}-8y^'+16y=0,y(0)=4,y(1)=5 is y=4e^{4t}+(5-4e^4)e^{4t-4}t