What is the solution for 49y^{''}+42y^'+9y=0,y(0)=7,y^'(0)=1 ?

The solution for 49y^{''}+42y^'+9y=0,y(0)=7,y^'(0)=1 is y=7e^{-(3t)/7}+4e^{-(3t)/7}t

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49y^{''}+42y^'+9y=0,y(0)=7,y^'(0)=1

49 y^{^{''}} + 42 y^{^{'}} + 9 y = 0, y (0) = 7, y^{^{'}} (0) = 1

y = 7 e^{- \frac{3 t}{7}} + 4 e^{- \frac{3 t}{7}} t

Solution steps

49 y^{''} (t) + 42 y^{'} (t) + 9 y = 0

Solve linear ODE:

y = 7 e^{- \frac{3 t}{7}} + 4 e^{- \frac{3 t}{7}} t

y = 7 e^{- \frac{3 t}{7}} + 4 e^{- \frac{3 t}{7}} t

y^{^{''''}} - 6 y^{^{'''}} + 5 y^{^{''}} = 0

- 2 y^{^{''}} + 6 y^{^{'}} + 5 y = 0

r^{2} y^{^{''}} + y^{^{'}} - n^{2} y = 0

y^{^{''}} - 5 y^{^{'}} + 4 y = 0, y (0) = - 1, y^{^{'}} (0) = - 5

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 4, y (1) = 5

What is the solution for 49y^{''}+42y^'+9y=0,y(0)=7,y^'(0)=1 ?
The solution for 49y^{''}+42y^'+9y=0,y(0)=7,y^'(0)=1 is y=7e^{-(3t)/7}+4e^{-(3t)/7}t