InterviewSolution
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InterviewSolution
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The integrating factor of differential equation `(dy)/(dx)+y=(1+y)/(x)"is"`A. `(x)/(x^(x)`B. `(e^(x))/(x)`C. `xe^(x)`D. `e^(x)` |
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Answer» Given that, `" "(dy)/(dx)+y=(1+y)/(x)` `rArr" "(dy)/(dx)=(1+y)/(x)-y` `rArr" "(dy)/(dx)=(1+y-xy)/(x)` `rArr" "(dy)/(dx)=(1)/(x)+(y(1-x))/(x)` `rArr" "(dy)/(dx)-((1-x)/(x))y=(1)/(x)` Here, `" "P=(-(1-x))/(x),Q=(1)/(x)` `" "IF=e^(intPdx)=e^(-int(1-x)/(x)dx)=e^(int(x-1)/(x)dx)` `" "=e^(int(1-(1)/(x))dx` `" "e^(intx-logx)` `" "=e^(x)*e^(log((1)/(x)))` `" "=e^(x)*(1)/(x)` |
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