How do you Solve the second order differential equitation y plus 3y equals 0?

Answer 1

This is not a second order equation as both the y terms are only to the first order. You may have meant y2 + 3y = 0. I will put the solution to both below:

FIRST ORDER EQUATION

y + 3y = 0
4y = 0 (add the two y terms)
y = 0 (divide by 4 on both sides)

By inspection we can see that it must be right as there is no number you can add to three times itself that would give 0 other than 0 itself.

SECOND ORDER EQUATION

y2 + 3y = 0
y(y + 3) = 0 (take out a common y multiplier)
Now you must recognize that for the answer on the right to equal zero, one of the two terms on the left must equal zero (because 0 x anything = 0). So either y must equal zero or (y+3) must be zero.
Therefor either y = 0 or (y+3) = 0 must be true.
So we know that the two possible values for y that would make the equation true are
y = 0 OR y = -3 (since it is a second order equation it must have two possible answers).

Test it:

if y=0:
02 + 3(0) = 0 + 0 = 0
CONFIRMED

if y=-3:
(-3)2 +3(-3) = 9 + (-9) = 9 - 9 = 0
CONFIRMED

So the answer is: y = 0 or y = -3.