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Which of the Following Pairs Forms a Fundamental Set of Solutions

Question 41

Multiple Choice

Which of the following pairs forms a fundamental set of solutions of the Cauchy Euler differential equation  Which of the following pairs forms a fundamental set of solutions of the Cauchy Euler differential equation   . A)    \{\cos (6 \ln x) , \sin (6 \ln x) \}   B)    \left\{x^{6} \cos (\ln x) , x^{6} \sin (\ln x) \right\}   C)    \{\ln (\cos (6 x) ) , \ln (\sin (6 x) ) \}   D)    \left\{x^{-6}, x^{6}\right\}   E)    \{\cos (\ln (6 x) ) , \sin (\ln (6 x) ) \} .


A) {cos(6lnx) ,sin(6lnx) } \{\cos (6 \ln x) , \sin (6 \ln x) \}
B) {x6cos(lnx) ,x6sin(lnx) } \left\{x^{6} \cos (\ln x) , x^{6} \sin (\ln x) \right\}
C) {ln(cos(6x) ) ,ln(sin(6x) ) } \{\ln (\cos (6 x) ) , \ln (\sin (6 x) ) \}
D) {x6,x6} \left\{x^{-6}, x^{6}\right\}
E) {cos(ln(6x) ) ,sin(ln(6x) ) } \{\cos (\ln (6 x) ) , \sin (\ln (6 x) ) \}

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