What is the solution for (d^2y)/(dx^2)-12(dy)/(dx)+52y=0 ?

The solution for (d^2y)/(dx^2)-12(dy)/(dx)+52y=0 is y=e^{6x}(c_{1}cos(4x)+c_{2}sin(4x))

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(d^2y)/(dx^2)-12(dy)/(dx)+52y=0

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 52 y = 0

y = e^{6 x} (c_{1} cos (4 x) + c_{2} sin (4 x))

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 52 y = 0

Solve linear ODE:

y = e^{6 x} (c_{1} cos (4 x) + c_{2} sin (4 x))

y = e^{6 x} (c_{1} cos (4 x) + c_{2} sin (4 x))

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

y^{^{''}} - 3 y^{^{'}} + (2.25 + a) y = 0, y (0) = 0

y^{^{''}} - 18 y^{^{'}} + 81 y = 0, y (0) = 0, y^{^{'}} (0) = 6

2 y^{^{''}} + 1000 y^{^{'}} + 2000000 y = 0

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

What is the solution for (d^2y)/(dx^2)-12(dy)/(dx)+52y=0 ?
The solution for (d^2y)/(dx^2)-12(dy)/(dx)+52y=0 is y=e^{6x}(c_{1}cos(4x)+c_{2}sin(4x))