Find a general solution of y" + 4y = 0.

Step-by-step explanation:

It is a linear homogeneous differential equation with constant coefficients:

y" + 4y = 0

Its characteristic equation:

r^2+4=0

r1=2i

r2=-2i

We use these roots in order to find the general solution:

all it means is function 3

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is