InterviewSolution
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InterviewSolution
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If `y = 3 cos (log x) + 4 sin (log x)`, show that `x^2y_2+xy_1+y=0` |
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Answer» `y=3" cos"(log x)+4" sin"(log x) " "`...(1) `impliesy_(1)=(d)/(dx)[3" cos"(log x) +4 sin (log x)]` `= -(3" sin"(log x))/(x)+(4" cos"(log x))/(x) ` `impliesxy_(1)= -3 "sin"(log x)+4cos(log x)` Again differentiate both sides w.r.t.x `x*y_(2)+y_(1)*1=(3cos(logx))/(x)-(4sin(log x))/(x)` `implies x^(2)y_(2)+xy_(1)= -[3cos(logx)+4sin(logx)]= -y` ` " " `from equation (1) `implies x^(2)y_(2)+xy_(1)+y=0 " " ` Hence proved. |
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