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

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

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(d^2y)/(dx^2)(1)-(dy)/(dx)(1)-2y=0

\frac{d ^{2} y}{d x ^{2}} (1) - \frac{d y}{d x} (1) - 2 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} (1) - \frac{d y}{d x} (1) - 2 y = 0

Solve linear ODE:

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

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

y^{^{'''}} - 15 y^{^{''}} + 62 y^{^{'}} - 72 y = 0

y^{^{''}} + 2 y^{^{'}} = - y

y^{^{''}} + y = 0, y^{^{'}} (0) = - 5

y^{^{''}} + y^{^{'}} = 0, y (\frac{π}{3}) = 0, y^{^{'}} (\frac{π}{3}) = 2

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

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