What is the solution for y^{''}-6y^'+9y=0,y(0)=2,y^'(0)=0 ?

The solution for y^{''}-6y^'+9y=0,y(0)=2,y^'(0)=0 is y=2e^{3t}-6e^{3t}t

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y^{''}-6y^'+9y=0,y(0)=2,y^'(0)=0

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 0

y = 2 e^{3 t} - 6 e^{3 t} t

Solution steps

y^{''} (t) - 6 y^{'} (t) + 9 y = 0

Solve linear ODE:

y = 2 e^{3 t} - 6 e^{3 t} t

y = 2 e^{3 t} - 6 e^{3 t} t

\int \frac{8}{4 + x ^{2}} d x

\frac{\partial}{\partial x} (x^{3} e^{x^{2} + y} - 12 y^{2})

y = - 2 x sin (x^{2})

\frac{s - 3}{s ^{2} - 3 s + 2}

x \to 10 lim (\frac{10 x}{2 x + 5})

What is the solution for y^{''}-6y^'+9y=0,y(0)=2,y^'(0)=0 ?
The solution for y^{''}-6y^'+9y=0,y(0)=2,y^'(0)=0 is y=2e^{3t}-6e^{3t}t