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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

9 y^{^{''}} - 6 y^{^{'}} + y = 0, y (0) = 3, y^{^{'}} (0) = 4

y^{^{''}} + \frac{16}{9} y = 0

u, \frac{d ^{2} u}{d x ^{2}} = u

16 y^{^{''}} + 8 y^{^{'}} + 5 y = 0

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