Tricky Separable Differential Equation Please guide me: y′+ay+b=0 (a not zero) is supposed to be separable and has solution y = ce^(-ax) - b/a Here is my start to this problem: (dy)/(dx) + ay = -b is as far as I can go with this. How should I go about separating x and

Paxton Hoffman 2022-07-18 Answered
Tricky Separable Differential Equation
Please guide me:
y + a y + b = 0
(a not zero) is supposed to be separable and has solution
y = c e a x b a
Here is my start to this problem:
d y d x + a y = b is as far as I can go with this. How should I go about separating x and
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Answers (2)

autarhie6i
Answered 2022-07-19 Author has 18 answers
d y d x + a y + b = 0
d y d x = a y b
d y a y + b = d x
Now, can you solve this?
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Bruno Thompson
Answered 2022-07-20 Author has 9 answers
We can take the differential equation
y + a y + b = 0
and write
y + a y = b
then multiply by e a x
e a x y + a e a x y = 5 e a x
Now the term on the left becomes
( y e a x ) = 5 e a x .
Next antidifferentiate and solve for y.
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