TS EAMCET · Maths · Differential Equations
\(y=A e^x+B e^{2 x}+C e^{3 x}\) satisfies the differential equation
- A \(y^{\prime \prime \prime}-6 y^{\prime \prime}+11 y^{\prime}-6 y=0\)
- B \(v^{\prime \prime \prime}+6 v^{\prime \prime}+11 v^{\prime}+6 v=0\)
- C \(y^{\prime \prime \prime}+6 y^{\prime \prime}-11 y^{\prime}+6 y=0\)
- D \(y^{\prime \prime \prime}-6 y^{\prime \prime}-11 y^{\prime}+6 y=0\)
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)…
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