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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{'}} = - 3 y + e^{- 2 x}

\frac{d}{d x} (\frac{x ^{2} + 1}{x - 2})

\int_{- 2}^{- 1} \frac{1}{x} d x

\int_{- 1}^{1} x^{2} + 1 d x

f (x) = x^{2} - 2, at x = a

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