What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)+5y=0 ?

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

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(d^2y)/(dx^2)-4(dy)/(dx)+5y=0

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 5 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 5 y = 0

Solve linear ODE:

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

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

81 y^{^{''}} + 72 y^{^{'}} + 16 y = 0

y^{^{''}} + y^{^{'}} + 1.25 y = 0

121 y^{^{''}} + 88 y^{^{'}} + 16 y = 0

y^{^{'''}} - 4 y^{^{''}} + 3 y^{^{'}} = 0

y^{^{''}} - y^{^{'}} - 56 y = 0, y (0) = - 5, y^{^{'}} (0) = 5

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