Use reduction of order. Given a solution , look for a second solution of the form .
Compute the first two derivatives of :
Substitute them into the ODE:
Now substitute and you end up with a linear ODE:
Multiply through both sides by (if you're familiar with the integrating factor method, this is it):
Bear in mind that in order to do this, we require . Just to avoid having to deal with absolute values later, let's further assume .
Notice that the left side is the derivative of a product,
Integrate both sides with respect to :
Solve for :
Solve for by integrating both sides:
Integrate by parts:
Solve for :
But since is already accounted for, the second solution is just
Still, the general solution would be
Answer:
c is the right answer for the problem
Answer:
Step-by-step explanation:
(2005, 12,000) (2005, 12,000)
x1 y1 x2 y2
m= (12,250-1200) / (2010-2005) = 250/5 = 50/1 = or 50
Answer:
K=4
Step-by-step explanation:
4(K+2)=32-2k
4k+8=32-2k
+2k +2k
6k+8=32
-8 -8
6k=24
divide 6 from both sides
k=6
Answer:
d = 5
Step-by-step explanation:
-7d = -35
Note the equal sign, what you do to one side, you do to the other. Isolate the variable, d. Divide - 7 from both sides:
(-7d)/-7 = (-35)/-7
d = -35/-7
d = 35/7
d = 5
d = 5 is your answer.
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