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

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

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

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

y = e^{x} (c_{1} cos (3 x) + c_{2} sin (3 x))

Solution steps

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

Solve linear ODE:

y = e^{x} (c_{1} cos (3 x) + c_{2} sin (3 x))

y = e^{x} (c_{1} cos (3 x) + c_{2} sin (3 x))

x^{^{''}} + 2 x^{^{'}} - 3 x = 0, x (0) = 1, x^{^{'}} (0) = - 2

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

y^{^{''}} - 3 y^{^{'}} - 4 y = 0, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} - 25 y = 0, y (0) = 1, y^{^{'}} (0) = 3

y^{^{''}} + 25 y = 0, y (\frac{π}{10}) = - 3, y (π) = - 8

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