COMEDK · Maths · 32. Differential Equations
The differential equation of \(y=a e^{b x+c}\) is
- A \(y_{2}=y_{1}+y\)
- B \(y_{2}^{2}=y y_{1}\)
- C \(y_{1}^{2}=y y_{2}\)
- D \(y^{2}=y_{1} y_{2}\)
Answer & Solution
Correct Answer
(C) \(y_{1}^{2}=y y_{2}\)
Step-by-step Solution
Detailed explanation
We have, \(y=a e^{b x+c}...(i)\) Differentiating Eq. (i) w.r.t. \(x\), we get \(y_{1}=a\left(e^{b x+c}\right) b=b\left(a e^{b x+c}\right)=b y...(ii)\) Again differentiating Eq. (ii) w.r.t. \(x\), we get \(y_{2}=b y_{1}...(iii)\) From Eq. (iii) and Eq. (i), we have…
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