What is the solution for (d^2y)/(dx^2)-8(dy)/(dx)+17y=0 ?

The solution for (d^2y)/(dx^2)-8(dy)/(dx)+17y=0 is y=e^{4x}(c_{1}cos(x)+c_{2}sin(x))

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(d^2y)/(dx^2)-8(dy)/(dx)+17y=0

\frac{d ^{2} y}{d x ^{2}} - 8 \frac{d y}{d x} + 17 y = 0

y = e^{4 x} (c_{1} cos (x) + c_{2} sin (x))

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 8 \frac{d y}{d x} + 17 y = 0

Solve linear ODE:

y = e^{4 x} (c_{1} cos (x) + c_{2} sin (x))

y = e^{4 x} (c_{1} cos (x) + c_{2} sin (x))

x^{^{'''}} + 9 x^{^{''}} + 15 x^{^{'}} - 25 x = 0

2 y^{^{''}} - y^{^{'}} - 2 y = 0

a y^{^{''}} + b y^{^{'}} + cy = 0, y (0) = 0

y^{^{''}} - 10 y^{^{'}} + 41 y = 0, y (0) = 10, y^{^{'}} (0) = 7

(d^{3} + 6 d^{2} + 11 d + 6) y = 0

What is the solution for (d^2y)/(dx^2)-8(dy)/(dx)+17y=0 ?
The solution for (d^2y)/(dx^2)-8(dy)/(dx)+17y=0 is y=e^{4x}(c_{1}cos(x)+c_{2}sin(x))