What is the solution for (d^2y)/(dx^2)(4)+(dy)/(dx)(5)+y=0 ?

The solution for (d^2y)/(dx^2)(4)+(dy)/(dx)(5)+y=0 is y=c_{1}e^{-x/4}+c_{2}e^{-x}

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(d^2y)/(dx^2)(4)+(dy)/(dx)(5)+y=0

\frac{d ^{2} y}{d x ^{2}} (4) + \frac{d y}{d x} (5) + y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} (4) + \frac{d y}{d x} (5) + y = 0

Solve linear ODE:

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

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

y^{^{''}} + 4 y^{^{'}} - 32 y = 0, y (0) = - 3

x^{^{'''}} + x^{^{''}} - 72 x^{^{'}} = 0

y^{^{''''}} = 256 y

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

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

What is the solution for (d^2y)/(dx^2)(4)+(dy)/(dx)(5)+y=0 ?
The solution for (d^2y)/(dx^2)(4)+(dy)/(dx)(5)+y=0 is y=c_{1}e^{-x/4}+c_{2}e^{-x}