What is the solution for (d^2y)/(dx^2)+15(dy)/(dx)+56y=0 ?

The solution for (d^2y)/(dx^2)+15(dy)/(dx)+56y=0 is y=c_{1}e^{-7x}+c_{2}e^{-8x}

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(d^2y)/(dx^2)+15(dy)/(dx)+56y=0

\frac{d ^{2} y}{d x ^{2}} + 15 \frac{d y}{d x} + 56 y = 0

y = c_{1} e^{- 7 x} + c_{2} e^{- 8 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 15 \frac{d y}{d x} + 56 y = 0

Solve linear ODE:

y = c_{1} e^{- 7 x} + c_{2} e^{- 8 x}

y = c_{1} e^{- 7 x} + c_{2} e^{- 8 x}

y^{^{''}} + 4 y^{^{'}} + k y = 0

y^{^{''}} + 4 y = 0, y (0) = 6, y^{^{'}} (0) = - 6

y^{^{''}} + 7 y^{^{'}} + 20 y = 0

2 y^{^{''}} + 14 y^{^{'}} + 12 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 4 y^{^{'}} - 8 y = 0

What is the solution for (d^2y)/(dx^2)+15(dy)/(dx)+56y=0 ?
The solution for (d^2y)/(dx^2)+15(dy)/(dx)+56y=0 is y=c_{1}e^{-7x}+c_{2}e^{-8x}