What is the solution for 3(d^2y)/(dx^2)+4(dy)/(dx)+y=0 ?

The solution for 3(d^2y)/(dx^2)+4(dy)/(dx)+y=0 is y=c_{1}e^{-x/3}+c_{2}e^{-x}

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

3 \frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + y = 0

y = c_{1} e^{- \frac{x}{3}} + c_{2} e^{- x}

Solution steps

3 \frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{x}{3}} + c_{2} e^{- x}

y = c_{1} e^{- \frac{x}{3}} + c_{2} e^{- x}

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (ln (2)) = 2, y (0) = 0

D^{2} (D^{2} - 4 D + 5)^{3} y = 0

20 y^{^{''}} + 27 y^{^{'}} + 9 y = 0, y (0) = 0, y^{^{'}} (0) = 8

3 y^{^{''}} + 2 y^{^{'}} + \frac{y}{4} = 0

y^{^{''}} + 8 y^{^{'}} - 9 y = 0, y (1) = 1, y^{^{'}} (1) = 1

What is the solution for 3(d^2y)/(dx^2)+4(dy)/(dx)+y=0 ?
The solution for 3(d^2y)/(dx^2)+4(dy)/(dx)+y=0 is y=c_{1}e^{-x/3}+c_{2}e^{-x}