Differential Equations Question 232
Question: A differential equation associated with the primitive $ y=a+be^{5x}+c{e^{-~7x}} $ is
Options:
A) $ y_3+2y_2-y_1=0 $
B) $ y_3+2y_2-35y_1=0 $
C) $ 4y_3+5y_2-20y_1=0 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ y=a+be^{5x}+c{e^{-7x}} $
- (i)
$ \therefore $ $ y_1=0+5be^{5x}-7c{e^{-7x}} $
Dividing by $ ye^{5x} $ , we get: $ {e^{-5x}}y_1=5b-7c{e^{-12x}} $ Again differentiating both sides w.r.t.x, we get $ {e^{-5x}}.y_2+y_1(-5){e^{-5x}}=0+84c{e^{-12x}} $
Dividing by $ {e^{-12x}} $ . We get: $ e^{7x}(y_2-5y_1)=84c $ Differentiating both sides w.r.t.x, we get $ e^{7x}(y_3-5y_2)+(y_2-5y_1).7e^{7x}=0 $
$ \Rightarrow y_3+2y_2-35y_1=0 $
BETA
