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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} - 5 y = 0, y (0) = - 2, y (2) = 10

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y (0) = 0, y^{^{'}} (0) = 1

2 y^{^{''}} - 12 y^{^{'}} + 18 y = 0

y^{^{''}} + 4 y = 0

y^{^{''}} + 40 y^{^{'}} + 6250 y = 0

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