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TS EAMCET · Maths · Differential Equations

\(y=A e^x+B e^{2 x}+C e^{3 x}\) satisfies the differential equation

  1. A \(y^{\prime \prime \prime}-6 y^{\prime \prime}+11 y^{\prime}-6 y=0\)
  2. B \(v^{\prime \prime \prime}+6 v^{\prime \prime}+11 v^{\prime}+6 v=0\)
  3. C \(y^{\prime \prime \prime}+6 y^{\prime \prime}-11 y^{\prime}+6 y=0\)
  4. D \(y^{\prime \prime \prime}-6 y^{\prime \prime}-11 y^{\prime}+6 y=0\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(y^{\prime \prime \prime}-6 y^{\prime \prime}+11 y^{\prime}-6 y=0\)

Step-by-step Solution

Detailed explanation

Given that, \( y=A e^x+B e^{2 x}+C e^{3 x} \) ...(i) On differentiating both sides w.r.t. \(x\), we get \( y^{\prime}=A e^x+2 B e^{2 x}+3 C e^{3 x} \) From Eq. (i)…