What is the solution for y^{''}-6y^'+9y=0,y(0)=4,y^'(0)=0 ?

The solution for y^{''}-6y^'+9y=0,y(0)=4,y^'(0)=0 is y=4e^{3t}-12e^{3t}t

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y^{''}-6y^'+9y=0,y(0)=4,y^'(0)=0

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 4, y^{^{'}} (0) = 0

y = 4 e^{3 t} - 12 e^{3 t} t

Solution steps

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

Solve linear ODE:

y = 4 e^{3 t} - 12 e^{3 t} t

y = 4 e^{3 t} - 12 e^{3 t} t

\int_{- \frac{1}{3}}^{0} \frac{3}{4} (1 - x^{2}) d x

x + x^{2} + ln (x)

x \to + 2 π lim (f (x))

ln (x^{3} + 3 x)

\frac{d x}{d y} = 5 x + y

What is the solution for y^{''}-6y^'+9y=0,y(0)=4,y^'(0)=0 ?
The solution for y^{''}-6y^'+9y=0,y(0)=4,y^'(0)=0 is y=4e^{3t}-12e^{3t}t