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Differential Equations Question?
Hello, I'm currently working on a Differential Equation Question.
The question goes as such
Find y as a function of t if
49y″−112y′+80y=0,
y(3)=9, y′(3)=4.
y=?
Any help is greatly appreciated. Thank you in advance!
2 Answers
- ViolaLv 53 years agoFavorite Answer
So take y = e^nt so that y' = ny and y'' = n²y.
Then the differential equation can be reduced to the quadratic
49n² - 112n + 80 = 0
whose solutions are n = 1.4 +/- 0.2i.
In other words, the general solution will be y = e^1.4t (A cos 0.2t + B sin 0.2t) for constants A and B which, at present, could be anything.
But, we're given two boundary conditions, which will enable us to identify the two unknowns A and B. Can I now leave it to you to solve these simultaneous equations and complete the answer?
- Anonymous3 years ago
Yeah, I think I got it from here