InterviewSolution
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InterviewSolution
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The solution of differential equation `(dy)/(dx)+(2xy)/(1+x^(2))=(1)/(1+x^(2))^(2)"is"`A. `y(1+x^(2))=C+tan^(-1)x`B. `(y)/(1+x^(2))=C+tan^(-1)x`C. `y log (1+x^(2))=C+tan^(-1)x`D. `(1+x^(2))=C+sin^(-1)x` |
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Answer» Given that, `" "(dy)/(dx)=(2xy)/(1+x^(2))=(1)/((1+x^(2))^(2))` Here, `" "P=(2x)/(1+x^(2)) and Q = (1)/((1+x^(2))^(2))` which is a linear differential equation. `therefore " "IF=e^(int(2x)/(1+x^(2))dx)` Put `" "1+x^(2)=trArr2xdx=dt` `therefore " "IF=e^(int(dt)/(t))=e^(logt)=e^(log(1+x^(2)))=1+x^(2)` The general solution is `" "y*(1+x^(2))=int(1+x^(2))(1)/((1+x^(2))^(2))+C` `rArr" "y(1+x^(2))=int(1)/(1+x^(2))dx+C` `rArr" "y(1+x^(2))=tan^(-1)x+C` |
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