What is the solution for y^{''}+10.5y=0 ?

The solution for y^{''}+10.5y=0 is y=c_{1}cos(sqrt(21/2)t)+c_{2}sin(sqrt(21/2)t)

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y^{''}+10.5y=0

y^{^{''}} + 10.5 y = 0

y = c_{1} cos (\frac{21}{2} t) + c_{2} sin (\frac{21}{2} t)

Solution steps

y^{''} (t) + 10.5 y = 0

Solve linear ODE:

y = c_{1} cos (\frac{21}{2} t) + c_{2} sin (\frac{21}{2} t)

y = c_{1} cos (\frac{21}{2} t) + c_{2} sin (\frac{21}{2} t)

\frac{d ^{2} y}{d x ^{2}} + 7 \frac{d y}{d x} - 12 y = 0

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

y^{^{''''}} + 4 y^{^{'''}} + y^{^{''}} - 5 y^{^{'}} + y = 0

y^{^{''}} + 3 y^{^{'}} - 3 y = 0

x^{^{''}} + 2 x^{^{'}} + 1^{2} x = 0

What is the solution for y^{''}+10.5y=0 ?
The solution for y^{''}+10.5y=0 is y=c_{1}cos(sqrt(21/2)t)+c_{2}sin(sqrt(21/2)t)