What is the solution for (8d^2+12d+5)y=0 ?

The solution for (8d^2+12d+5)y=0 is y=e^{-(3x)/4}(c_{1}cos(x/4)+c_{2}sin(x/4))

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(8d^2+12d+5)y=0

(8 d^{2} + 12 d + 5) y = 0

y = e^{- \frac{3 x}{4}} (c_{1} cos (\frac{x}{4}) + c_{2} sin (\frac{x}{4}))

Solution steps

(8 d^{2} + 12 d + 5) y = 0

Solve linear ODE:

y = e^{- \frac{3 x}{4}} (c_{1} cos (\frac{x}{4}) + c_{2} sin (\frac{x}{4}))

y = e^{- \frac{3 x}{4}} (c_{1} cos (\frac{x}{4}) + c_{2} sin (\frac{x}{4}))

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

3 x y^{^{''}} - 2 x y^{^{'}} + 11 x y = 0

4 y^{^{''}} - y = 0, y (- 2) = 1, y^{^{'}} (- 2) = 1

\frac{d ^{2} x}{d t ^{2}} + 2 a \frac{d x}{d t} + b^{2} x = 0

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y = e^{3 x}

What is the solution for (8d^2+12d+5)y=0 ?
The solution for (8d^2+12d+5)y=0 is y=e^{-(3x)/4}(c_{1}cos(x/4)+c_{2}sin(x/4))