What is the solution for 3(d^2y)/(dx^2)+6(dy)/(dx)+3y=0 ?

The solution for 3(d^2y)/(dx^2)+6(dy)/(dx)+3y=0 is y=c_{1}e^{-x}+c_{2}xe^{-x}

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3(d^2y)/(dx^2)+6(dy)/(dx)+3y=0

3 \frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 3 y = 0

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

Solution steps

3 \frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 3 y = 0

Solve linear ODE:

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

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

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

y^{^{'''}} - 7 y^{^{''}} + y^{^{'}} + 12 y = 0

y^{^{''}} - \frac{1}{4} y = 0, y (0) = 4, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = - 2

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 5, y^{^{'}} = 2

What is the solution for 3(d^2y)/(dx^2)+6(dy)/(dx)+3y=0 ?
The solution for 3(d^2y)/(dx^2)+6(dy)/(dx)+3y=0 is y=c_{1}e^{-x}+c_{2}xe^{-x}