What is the solution for y^{''}+10y+16y=0 ?

The solution for y^{''}+10y+16y=0 is y=c_{1}cos(sqrt(26)t)+c_{2}sin(sqrt(26)t)

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y^{''}+10y+16y=0

y^{^{''}} + 10 y + 16 y = 0

y = c_{1} cos (26 t) + c_{2} sin (26 t)

Solution steps

y^{''} (t) + 10 y + 16 y = 0

Solve linear ODE:

y = c_{1} cos (26 t) + c_{2} sin (26 t)

y = c_{1} cos (26 t) + c_{2} sin (26 t)

8 \frac{d ^{2} y}{d t ^{2}} + 12 \frac{d y}{d t} + 5 y = 0

\frac{d ^{2} y}{d t ^{2}} - 18 \frac{d y}{d t} + 81 y = 0

y^{^{'''}} + 4 y^{^{''}} - 25 y^{^{'}} - 28 y = 0

y^{^{''}} + 3 y^{^{'}} + 6 \cdot y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 8.1, y^{^{'}} (0) = 3.9

What is the solution for y^{''}+10y+16y=0 ?
The solution for y^{''}+10y+16y=0 is y=c_{1}cos(sqrt(26)t)+c_{2}sin(sqrt(26)t)