find the general solution to the differential equation a y4y

find the general solution to the differential equation

a) y\'\'+4y\'+3y=0

b) y\'\'+10y\'+25y=0

thank you

Solution

3. a) the auxiliary equation is of the form:

        D² + 4D + 3 = 0

        (D+3)(D+1) = 0

         D = -3 , D = -1

The general solution is given by:

y = C₁ e^(-3x) + C₂ e^(-x)

b) the auxiliary equation is of the form:

        D² + 10D + 25 = 0

        (D+5)(D+5) = 0

         D = -5 , D = -5

The general solution is given by:

y = C₁ e^(-5x) + C₂ xe^(-5x)