Question

25y′′−70y′+49y=0Find the general solution of the differential equation 

Answer 1

$$25y''−70y'+49y=0$$

Characteristic (auxiliary) equation

$$25r^2-70r+49=0$$

$$(5r-7)^2=0$$

$$r_{1,2}=1.4$$

The general solution is

$$y=C_1e^{1.4x}+C_2xe^{1.4x}$$