A) 4
B) 3
C) 2
D) 5
Correct Answer: B
Solution :
Given, \[y=({{c}_{1}}+{{c}_{2}})\cos (x+{{c}_{3}})-{{c}_{4}}{{e}^{x+{{c}_{5}}}}\] \[\Rightarrow \] \[y=({{c}_{1}}\cos {{c}_{3}}+{{c}_{2}}\cos {{c}_{3}})\cos x\] \[=({{c}_{1}}\sin {{c}_{3}}+{{c}_{2}}\sin {{c}_{3}})\sin x-{{c}_{4}}{{e}^{{{c}_{5}}}}{{e}^{x}}\] \[\Rightarrow \] \[y=A\cos x-B\sin x\cdot C{{e}^{x}}\] where, \[A={{c}_{1}}\cos {{c}_{3}}+{{c}_{2}}\cos {{c}_{3}}\] \[B={{c}_{1}}\sin {{c}_{3}}+{{c}_{2}}\sin {{c}_{3}}\] and \[C=-{{c}_{4}}{{e}^{{{c}_{5}}}}\] Which is an equation containing three arbitrary constant. Hence, the order of the differential equation is 3.
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