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

The solution for (d^2y)/(dx^2)+4(dy)/(dx)=-y is y=c_{1}e^{(-2+sqrt(3))x}+c_{2}e^{(-2-sqrt(3))x}

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

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} = - y

y = c_{1} e^{(- 2 + 3) x} + c_{2} e^{(- 2 - 3) x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} = - y

Solve linear ODE:

y = c_{1} e^{(- 2 + 3) x} + c_{2} e^{(- 2 - 3) x}

y = c_{1} e^{(- 2 + 3) x} + c_{2} e^{(- 2 - 3) x}

y^{^{''}} + 2 y^{^{'}} + 10 y = 0, y (0) = e^{- \frac{π}{6}}

\frac{d ^{3} y}{d t ^{3}} - \frac{d ^{2} y}{d t ^{2}} = 0

y^{^{''}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = \frac{18}{5}

64 y^{^{''}} + 16 y^{^{'}} + 50 y = 0

x^{^{''}} - (nπ)^{2} x = 0

What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)=-y ?
The solution for (d^2y)/(dx^2)+4(dy)/(dx)=-y is y=c_{1}e^{(-2+sqrt(3))x}+c_{2}e^{(-2-sqrt(3))x}