A) \[{{n}^{2}}y+\cos \,\,nx={{n}^{2}}(Cx+D)\]
B) \[{{n}^{2}}y-sin\,\,nx={{n}^{2}}(-Cx+D)\]
C) \[{{n}^{2}}y+\cos \,\,nx=\frac{Cx+D}{{{n}^{2}}}\]
D) None of these. [Where C and D are arbitrary constants]
Correct Answer: A
Solution :
[a] The differential equation is \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=\cos nx\] Integrating we get \[\frac{dy}{dx}=\frac{\sin nx}{n}+C\] ? (i) Integrating again \[y=-\frac{\cos nx}{{{n}^{2}}}+Cx+D\] \[\Rightarrow {{n}^{2}}y+\cos nx={{n}^{2}}(Cx+D)\]
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