微分方程式を入力してください。

The given differential equation is:

y'' - 10y' + 29y = 0

This is a second-order linear homogeneous differential equation with constant coefficients.

To solve this equation, we can use the characteristic equation method.

The characteristic equation for this differential equation is:

r^2 - 10r + 29 = 0

Solving the characteristic equation, we get:

r1 = 5 + √(25 - 29) = 5 + √(-4) = 5 + 2i r2 = 5 - √(25 - 29) = 5 - 2i

Since the roots are complex conjugates, the general solution of the differential equation is:

y(t) = C1 * e^(5t) * cos(2t) + C2 * e^(5t) * sin(2t)

Where C1 and C2 are arbitrary constants that can be determined using the initial conditions.

This is the general solution of the given second-order linear homogeneous differential equation with constant coefficients.