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

The solution for y^{'''}+9y^'=0,y(0)=7 is y=7-c_{2}+c_{2}cos(3t)+c_{3}sin(3t)

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

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

y = 7 - c_{2} + c_{2} cos (3 t) + c_{3} sin (3 t)

Solution steps

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

Solve linear ODE:

y = 7 - c_{2} + c_{2} cos (3 t) + c_{3} sin (3 t)

y = 7 - c_{2} + c_{2} cos (3 t) + c_{3} sin (3 t)

2 y^{^{''}} - 13 y^{^{'}} + 15 y = 0, y (0) = 0, y^{^{'}} (0) = 17.5

θ^{^{''}} (t) + \frac{9. 8 ^{2}}{80} θ (t) = 0

\frac{( \frac{d ^{2} f}{d x ^{2}} )}{f ( x )} = 1

y^{^{''}} = - 4 y, y (0) = 3, y^{^{'}} (0) = - 63

y^{^{''''}} - 15 y^{^{''}} + 54 y = 0

What is the solution for y^{'''}+9y^'=0,y(0)=7 ?
The solution for y^{'''}+9y^'=0,y(0)=7 is y=7-c_{2}+c_{2}cos(3t)+c_{3}sin(3t)