What is the solution for (d^2)/(dθ^2)(y(θ))+y(θ)=0 ?

The solution for (d^2)/(dθ^2)(y(θ))+y(θ)=0 is y(θ)=c_{1}cos(θ)+c_{2}sin(θ)

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(d^2)/(dθ^2)(y(θ))+y(θ)=0

\frac{d ^{2}}{d θ ^{2}} (y (θ)) + y (θ) = 0

y (θ) = c_{1} cos (θ) + c_{2} sin (θ)

Solution steps

\frac{d ^{2}}{d θ ^{2}} (y (θ)) + y (θ) = 0

Solve linear ODE:

y (θ) = c_{1} cos (θ) + c_{2} sin (θ)

y (θ) = c_{1} cos (θ) + c_{2} sin (θ)

x^{^{''}} + 2 x^{^{'}} + 10 x = 0

y^{^{'''}} - 3 y^{^{''}} - 4 y^{^{'}} + 12 y = 0

y^{^{''}} + y = 0, y (0) = sin (x)

9 \frac{d ^{2} y}{d t ^{2}} - 24 \frac{d y}{d t} + 16 y = 0

y^{^{''}} + 3 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 1

What is the solution for (d^2)/(dθ^2)(y(θ))+y(θ)=0 ?
The solution for (d^2)/(dθ^2)(y(θ))+y(θ)=0 is y(θ)=c_{1}cos(θ)+c_{2}sin(θ)