AP EAMCET · Maths · Differential Equations
Let \(c_1, c_2, c_3, c_4\) be arbitrary constants. The order of the differential equation, corresponding to \(y=c_1 e^x+\) \(\mathrm{c}_2 \mathrm{e}^{\log _{\mathrm{e}} \mathrm{x}}+\mathrm{c}_3 \sin ^2 \mathrm{x}-\mathrm{c}_4\left(\cos ^2 \mathrm{x}-1\right)\) is
- A 1
- B 2
- C 3
- D 4
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
\(\because y=c_1 e^x+c_2 e^{\log c x}+c_3 \sin ^2 x-c_4\left(\cos ^2 x-1\right)\) \(\Rightarrow y=c_1 e^x+c_2 x+\left(c_3+c_4\right) \sin ^2 x\) \(\Rightarrow y=c_1 e^x+c_2 x+c_3^{\prime} \sin ^2 x\) ...(i) where \(c_3^{\prime}=c_3+c_4\)…
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