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

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

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

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

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} e^{- x} + c_{4} x e^{- x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} e^{- x} + c_{4} x e^{- x}

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} e^{- x} + c_{4} x e^{- x}

\frac{d ^{2} f}{d x ^{2}} = a^{2} f (x)

y^{^{'}} = y^{^{''}}

2 y^{^{''}} + 4 y^{^{'}} - 7 y = 0

81 y^{^{''''}} = 16 y

\frac{d ^{2} x}{d t ^{2}} + 4 \frac{d x}{d t} + 5 x = 0

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