InterviewSolution
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InterviewSolution
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Find the general solution of each of the following differential equations: `(1)/(x)*(dy)/(dx)=tan^(-1)x` |
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Answer» Correct Answer - `y=(1)/(2)(x^(2)+1)tan^(-1)x-(1)/(2)x+C` `intdy = int (underset(I)(tan^(-1))x)underset(II)(x) dx rArr y=(tan^(-1)x)(x^(2))/(2)-int (1)/((1+x^(2)))*(x^(2))/(2)dx +C` `rArr y = (1)/(2)x^(2)(tan^(-1)x)-(1)/(2)int{((1+x^(2))-1)/((1+x^(2)))}dx +C.` `rArr y =(1)/(2)x^(2)(tan^(-1)x)-(1)/(2)int{1-(1)/((1+x^(2)))}dx +C`. |
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