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

The solution for y^{''}-8y^'+16y=0,y(0)=5,y^'(0)=0 is y=5e^{4t}-20e^{4t}t

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

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

y = 5 e^{4 t} - 20 e^{4 t} t

Solution steps

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

Solve linear ODE:

y = 5 e^{4 t} - 20 e^{4 t} t

y = 5 e^{4 t} - 20 e^{4 t} t

h \to 0 lim (\frac{h}{h ^{2} - 7 h + 1})

\frac{d}{d x} (10 0.6 x + 7)

f (x) = x^{2} + 40, at x = 3

\frac{d y}{d x} + 7 (tan (7 x)) y = 2 cos (7 x)

x \to - 4 lim (8 - x)

What is the solution for y^{''}-8y^'+16y=0,y(0)=5,y^'(0)=0 ?
The solution for y^{''}-8y^'+16y=0,y(0)=5,y^'(0)=0 is y=5e^{4t}-20e^{4t}t