What is the solution for 4(d^2y)/(dx^2)-16(dy)/(dx)+16y=0 ?

The solution for 4(d^2y)/(dx^2)-16(dy)/(dx)+16y=0 is y=c_{1}e^{2x}+c_{2}xe^{2x}

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4(d^2y)/(dx^2)-16(dy)/(dx)+16y=0

4 \frac{d ^{2} y}{d x ^{2}} - 16 \frac{d y}{d x} + 16 y = 0

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

Solution steps

4 \frac{d ^{2} y}{d x ^{2}} - 16 \frac{d y}{d x} + 16 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^{^{''}} + 2 y^{^{'}} - 4 y = 0

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 3

\frac{d ^{2} y}{d x ^{2}} = k^{2} y

9 y^{^{''}} + 17 y^{^{'}} - 2 y = 0

y^{^{''}} + 4 y^{^{'}} + 40 y = 0

What is the solution for 4(d^2y)/(dx^2)-16(dy)/(dx)+16y=0 ?
The solution for 4(d^2y)/(dx^2)-16(dy)/(dx)+16y=0 is y=c_{1}e^{2x}+c_{2}xe^{2x}