What is the solution for (d^2y)/(dx^2)-10(dy)/(dx)+29y=0 ?

The solution for (d^2y)/(dx^2)-10(dy)/(dx)+29y=0 is y=e^{5x}(c_{1}cos(2x)+c_{2}sin(2x))

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(d^2y)/(dx^2)-10(dy)/(dx)+29y=0

\frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} + 29 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} + 29 y = 0

Solve linear ODE:

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

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

y^{^{''}} + 10 y^{^{'}} + 16 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + k y^{^{'}} + 8 y = 0, y (0) = e^{2 x} sin (2 x)

y^{^{''}} - 10 y = 0

\frac{d ^{2} y}{d x ^{2}} + 25 y = 0

y^{^{''}} - y^{^{'}} - 20 y = 0, y (0) = 4, y^{^{'}} (0) = 29

What is the solution for (d^2y)/(dx^2)-10(dy)/(dx)+29y=0 ?
The solution for (d^2y)/(dx^2)-10(dy)/(dx)+29y=0 is y=e^{5x}(c_{1}cos(2x)+c_{2}sin(2x))