TS EAMCET · Maths · Differential Equations
If \(y=e^{a x}(\cos b x+\sin b x)\) satisfies the equation \(\frac{d^2 y}{d x^2}-K \frac{d y}{d x}+L y=0\), then \(L+b K=\)
- A 0
- B \((a+b)^2\)
- C \(a^2-b^2\)
- D \(a^2+b^2\)
Answer & Solution
Correct Answer
(B) \((a+b)^2\)
Step-by-step Solution
Detailed explanation
We have, \(y=e^{a x}(\cos b x+\sin b x)\) \(\frac{d y}{d x}=e^{a x}(-\sin b x \cdot b+\cos b x \cdot b)\) \(+a \cdot e^{a x}(\cos b x+\sin b x)\) \(\frac{d y}{d x}=b e^{a x}(\cos b x-\sin b x)+a y\) \(\ldots(\mathrm{i})\)…
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