What is the solution for (d^2y)/(dx^2)(1)+5y=0 ?

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

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(d^2y)/(dx^2)(1)+5y=0

\frac{d ^{2} y}{d x ^{2}} (1) + 5 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} (1) + 5 y = 0

Solve linear ODE:

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

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

\frac{d ^{2} x}{d t ^{2}} + 8 \frac{d x}{d t} + 16 x = 0

y^{^{'''}} + 2 y^{^{''}} - 10 y^{^{'}} + 4 y = 0

y^{^{'''}} - 2 y^{^{''}} - 4 y^{^{'}} = 0

y^{^{''}} - 14 y^{^{'}} + 65 y = 0, y (0) = 4, y^{^{'}} (0) = - 4

- a y^{^{''}} + b y^{^{'}} + cy = 0

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