What is the solution for ((d^2y)/(dx^2)-2(dy)/(dx)+5y)^3=0 ?

The solution for ((d^2y)/(dx^2)-2(dy)/(dx)+5y)^3=0 is y=e^x(c_{1}cos(2x)+c_{2}sin(2x))

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((d^2y)/(dx^2)-2(dy)/(dx)+5y)^3=0

(\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + 5 y)^{3} = 0

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

Solution steps

(\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + 5 y)^{3} = 0

Solve linear ODE:

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

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

y^{^{''}} - 11 y^{^{'}} - 24 y = 0

x^{^{''''}} + 2 x^{^{''}} + x = 0

27 \frac{d ^{3} y}{d x ^{3}} + y = 0

y^{^{''}} + 6 y^{^{'}} + 25 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

\frac{x ^{^{''}} + ( n - 1 ) x ^{^{'}}}{r} = 0

What is the solution for ((d^2y)/(dx^2)-2(dy)/(dx)+5y)^3=0 ?
The solution for ((d^2y)/(dx^2)-2(dy)/(dx)+5y)^3=0 is y=e^x(c_{1}cos(2x)+c_{2}sin(2x))