What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)+68y=0 ?

The solution for (d^2y)/(dx^2)-4(dy)/(dx)+68y=0 is y=e^{2x}(c_{1}cos(8x)+c_{2}sin(8x))

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(d^2y)/(dx^2)-4(dy)/(dx)+68y=0

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 68 y = 0

y = e^{2 x} (c_{1} cos (8 x) + c_{2} sin (8 x))

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 68 y = 0

Solve linear ODE:

y = e^{2 x} (c_{1} cos (8 x) + c_{2} sin (8 x))

y = e^{2 x} (c_{1} cos (8 x) + c_{2} sin (8 x))

x \to - 7 - lim (\frac{- 9 x}{x + 7})

\int \frac{x + 3}{x} d x

x \to 4 lim (25 - x^{2})

x \to 0 lim ((x + 1)^{2} - x^{2})

\frac{\partial}{\partial x} (x^{8} + x y^{5} + 5)

What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)+68y=0 ?
The solution for (d^2y)/(dx^2)-4(dy)/(dx)+68y=0 is y=e^{2x}(c_{1}cos(8x)+c_{2}sin(8x))