Question

y''-10y'+25y=0 find general solution of the given second order differential equation.

Answer 1

Let us consider DE

$$y''-10y'+25y=0$$

The characteristic equation is given by

$$k^2-10k+25=0$$

Roots:

$$k_1=5,\quad k_2=5$$

General solution

$$y(x)=C_1e^{5x}+C_2xe^{5x}$$