What is the solution for y^{''}-8y^'+16y=0,y(0)=7,y^'(0)=0 ?

The solution for y^{''}-8y^'+16y=0,y(0)=7,y^'(0)=0 is y=7e^{4t}-28e^{4t}t

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y^{''}-8y^'+16y=0,y(0)=7,y^'(0)=0

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 7, y^{^{'}} (0) = 0

y = 7 e^{4 t} - 28 e^{4 t} t

Solution steps

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

Solve linear ODE:

y = 7 e^{4 t} - 28 e^{4 t} t

y = 7 e^{4 t} - 28 e^{4 t} t

\frac{17}{160} x^{^{''}} + 0.4 x^{^{'}} + 2 x = 0

y^{^{'''}} + 9 y^{^{'}} = 0, y (0) = - 21

y^{^{'}} + 18 y^{^{''}} + 81 y = 0

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = 7

x^{^{''}} + 2 x^{^{'}} + 1000 x = 0, x (0) = 0.75, x^{^{'}} (0) = 0

What is the solution for y^{''}-8y^'+16y=0,y(0)=7,y^'(0)=0 ?
The solution for y^{''}-8y^'+16y=0,y(0)=7,y^'(0)=0 is y=7e^{4t}-28e^{4t}t