What is the solution for 1/2 (d^2y)/(dx^2)+6(dy)/(dx)+26y=0 ?

The solution for 1/2 (d^2y)/(dx^2)+6(dy)/(dx)+26y=0 is y=e^{-6x}(c_{1}cos(4x)+c_{2}sin(4x))

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1/2 (d^2y)/(dx^2)+6(dy)/(dx)+26y=0

\frac{1}{2} \frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 26 y = 0

y = e^{- 6 x} (c_{1} cos (4 x) + c_{2} sin (4 x))

Solution steps

\frac{1}{2} \frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 26 y = 0

Solve linear ODE:

y = e^{- 6 x} (c_{1} cos (4 x) + c_{2} sin (4 x))

y = e^{- 6 x} (c_{1} cos (4 x) + c_{2} sin (4 x))

y^{^{''}} - 2 y^{^{'}} - 3 y = 0, y (4) = - 17

y^{^{'''}} + (- 7) y^{^{''}} + 8 y^{^{'}} + 16 y = 0

y^{^{''}} + 2 y^{^{'}} + y = 0, y (1) = - x e^{x}

y^{^{''}} + a^{2} b^{2} y = 0

y^{^{''}} + 4 y^{^{'}} - 5 y = 0, y^{^{'}} (ln (2)) = 3, y (0) = 33

What is the solution for 1/2 (d^2y)/(dx^2)+6(dy)/(dx)+26y=0 ?
The solution for 1/2 (d^2y)/(dx^2)+6(dy)/(dx)+26y=0 is y=e^{-6x}(c_{1}cos(4x)+c_{2}sin(4x))