AP EAMCET · Maths · Differential Equations
The differential equation corresponding to the family of curves \(y=e^x(A \cos x+B \sin x)\) is
- A \(y^{\prime \prime}+y^{\prime}+y=0\)
- B \(y^{\prime \prime}+2 y^{\prime}+2 y=0\)
- C \(y^{\prime \prime}-2 y^{\prime}+2 y=0\)
- D \(y^{\prime \prime}-2 y^{\prime}-2 y=0\)
Answer & Solution
Correct Answer
(C) \(y^{\prime \prime}-2 y^{\prime}+2 y=0\)
Step-by-step Solution
Detailed explanation
Given, curve \(y=e^x(A \cos x+B \sin x)\) ...(i) So, \(y^{\prime}=e^x(-A \sin x+B \cos x)+e^x(A \cos x+B \sin x)\) \(\Rightarrow \quad y^{\prime}-y=e^x(-A \sin x+B \cos x)\) ...(ii) So, \(y^{\prime}-y^{\prime}=e^x(-A \cos x-B \sin x)\) \(+e^x(-A \sin x+B \cos x)\)…
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