What is the solution for (d^2x)/(dt^2)+xk+a=0 ?

The solution for (d^2x)/(dt^2)+xk+a=0 is x=c_{1}cos(sqrt(k)t)+c_{2}sin(sqrt(k)t)-a/k

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(d^2x)/(dt^2)+xk+a=0

\frac{d ^{2} x}{d t ^{2}} + x k + a = 0

x = c_{1} cos (k t) + c_{2} sin (k t) - \frac{a}{k}

Solution steps

\frac{d ^{2} x}{d t ^{2}} + x k + a = 0

Solve linear ODE:

x = c_{1} cos (k t) + c_{2} sin (k t) - \frac{a}{k}

x = c_{1} cos (k t) + c_{2} sin (k t) - \frac{a}{k}

y^{^{''}} - 2 y^{^{'}} + y = x^{\frac{1}{2}} e^{x}

y^{^{''}} + 2 y^{^{'}} + y = x^{2} - 5

y^{^{''}} - 2 y^{^{'}} = sin (x) + e^{x}

y^{^{''}} - 6 y^{^{'}} + 9 y = t^{2} e^{3 t}

y^{^{''}} - 25 y = cosh (5 x)

What is the solution for (d^2x)/(dt^2)+xk+a=0 ?
The solution for (d^2x)/(dt^2)+xk+a=0 is x=c_{1}cos(sqrt(k)t)+c_{2}sin(sqrt(k)t)-a/k