What is the solution for y^{''}-6y^'+9y=0,y(0)=1,y^'(0)=7 ?

The solution for y^{''}-6y^'+9y=0,y(0)=1,y^'(0)=7 is y=e^{3t}+4e^{3t}t

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

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

y = e^{3 t} + 4 e^{3 t} t

Solution steps

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

Solve linear ODE:

y = e^{3 t} + 4 e^{3 t} t

y = e^{3 t} + 4 e^{3 t} t

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

y^{^{''}} + y^{^{'}} + 4 y = 0, y (0) = 3, y^{^{'}} (0) = 0

y^{^{''}} - y^{^{'}} + 2 y = 0, y (0) = 5, y^{^{'}} (0) = 5

\frac{d ^{2} y}{d x ^{2}} + 9 \frac{d y}{d x} + 20 y = 0

y^{^{''}} + 12 y^{^{'}} + 27 y = 0, y (0) = 11, y^{^{'}} (0) = - 81

What is the solution for y^{''}-6y^'+9y=0,y(0)=1,y^'(0)=7 ?
The solution for y^{''}-6y^'+9y=0,y(0)=1,y^'(0)=7 is y=e^{3t}+4e^{3t}t