What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)+29y=0 ?

The solution for (d^2y)/(dx^2)-4(dy)/(dx)+29y=0 is y=e^{2x}(c_{1}cos(5x)+c_{2}sin(5x))

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(d^2y)/(dx^2)-4(dy)/(dx)+29y=0

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 29 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 29 y = 0

Solve linear ODE:

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

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

y^{^{'''}} - 5 y^{^{''}} + 3 y^{^{'}} + y = 0

64 y^{^{''}} + 112 y^{^{'}} + 49 y = 0

\frac{1}{16} x^{^{''}} + 2 x^{^{'}} + x = 0

y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = 6, y^{^{'}} (0) = 10

y^{^{''}} - 2 y^{^{'}} + 2 y = 0, y (π) = - 1, y (0) = 1

What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)+29y=0 ?
The solution for (d^2y)/(dx^2)-4(dy)/(dx)+29y=0 is y=e^{2x}(c_{1}cos(5x)+c_{2}sin(5x))