What is the solution for (d^2y)/(dx^2)-6(dy)/(dx)+25y=0 ?

The solution for (d^2y)/(dx^2)-6(dy)/(dx)+25y=0 is y=e^{3x}(c_{1}cos(4x)+c_{2}sin(4x))

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(d^2y)/(dx^2)-6(dy)/(dx)+25y=0

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 25 y = 0

y = e^{3 x} (c_{1} cos (4 x) + c_{2} sin (4 x))

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 25 y = 0

Solve linear ODE:

y = e^{3 x} (c_{1} cos (4 x) + c_{2} sin (4 x))

y = e^{3 x} (c_{1} cos (4 x) + c_{2} sin (4 x))

y^{^{''}} + 7 y^{^{'}} - 10 y = 0

64 y^{^{''}} + 48 y^{^{'}} + 9 y = 0

x^{^{''}} + 2 x^{^{'}} + 2 x = 0, x (0) = 1, x^{^{'}} (0) = 0

y^{^{'''}} + 5 y^{^{''}} + 4 y^{^{'}} = 0

y^{^{''}} + 6 y^{^{'}} + 25 y = 0, y (0) = 4, y^{^{'}} (0) = - 11

What is the solution for (d^2y)/(dx^2)-6(dy)/(dx)+25y=0 ?
The solution for (d^2y)/(dx^2)-6(dy)/(dx)+25y=0 is y=e^{3x}(c_{1}cos(4x)+c_{2}sin(4x))