What is the solution for (d^2y)/(dx^2)-10(dy)/(dx)+26y=0 ?

The solution for (d^2y)/(dx^2)-10(dy)/(dx)+26y=0 is y=e^{5x}(c_{1}cos(x)+c_{2}sin(x))

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(d^2y)/(dx^2)-10(dy)/(dx)+26y=0

\frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} + 26 y = 0

y = e^{5 x} (c_{1} cos (x) + c_{2} sin (x))

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} + 26 y = 0

Solve linear ODE:

y = e^{5 x} (c_{1} cos (x) + c_{2} sin (x))

y = e^{5 x} (c_{1} cos (x) + c_{2} sin (x))

y^{^{'}} = 8 y^{^{''}}

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

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = - 3, y^{^{'}} (0) = 1

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y (0) = 2, y^{^{'}} (0) = 5

9 y^{^{''}} - 12 y^{^{'}} + 4 y = 0, y (0) = 4, y^{^{'}} (0) = - 1

What is the solution for (d^2y)/(dx^2)-10(dy)/(dx)+26y=0 ?
The solution for (d^2y)/(dx^2)-10(dy)/(dx)+26y=0 is y=e^{5x}(c_{1}cos(x)+c_{2}sin(x))