What is the solution for (d^2y)/(dx^2)+11(dy)/(dx)+28y=0 ?

The solution for (d^2y)/(dx^2)+11(dy)/(dx)+28y=0 is y=c_{1}e^{-4x}+c_{2}e^{-7x}

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(d^2y)/(dx^2)+11(dy)/(dx)+28y=0

\frac{d ^{2} y}{d x ^{2}} + 11 \frac{d y}{d x} + 28 y = 0

y = c_{1} e^{- 4 x} + c_{2} e^{- 7 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 11 \frac{d y}{d x} + 28 y = 0

Solve linear ODE:

y = c_{1} e^{- 4 x} + c_{2} e^{- 7 x}

y = c_{1} e^{- 4 x} + c_{2} e^{- 7 x}

y^{^{''''}} + y^{^{'''}} - 5 y^{^{''}} - 3 y^{^{'}} + \frac{1}{2} y = 0

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

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

y^{^{''}} - 10 y^{^{'}} + 50 y = 0

5 \cdot x^{^{''}} + x^{^{'}} + 10 \cdot x = 0

What is the solution for (d^2y)/(dx^2)+11(dy)/(dx)+28y=0 ?
The solution for (d^2y)/(dx^2)+11(dy)/(dx)+28y=0 is y=c_{1}e^{-4x}+c_{2}e^{-7x}