What is the solution for (d^2y)/(dx^2)+6(dy)/(dx)+25y=0 ?

The solution for (d^2y)/(dx^2)+6(dy)/(dx)+25y=0 is y=e^{-3x}(c_{1}cos(4x)+c_{2}sin(4x))

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(d^2y)/(dx^2)+6(dy)/(dx)+25y=0

\frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 25 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 25 y = 0

Solve linear ODE:

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

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

y^{^{''}} + k^{2} y = 0

y^{^{''}} - 17 y^{^{'}} + 72 y = 0

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = 2

y^{^{'''}} = y^{^{'}}

9 y^{^{''}} - 12 y^{^{'}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = \frac{4}{3}

What is the solution for (d^2y)/(dx^2)+6(dy)/(dx)+25y=0 ?
The solution for (d^2y)/(dx^2)+6(dy)/(dx)+25y=0 is y=e^{-3x}(c_{1}cos(4x)+c_{2}sin(4x))