InterviewSolution
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InterviewSolution
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हल कीजिए- `(dy)/(dx) =x^(5) tan ^(-1)(x^(3)).` |
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Answer» दिया गया अवकल समीकरण है- `(dy)/(dx) =x^(5) tan ^(-1)(x^(3))` `implies dy =x^(5) tan ^(-1) (x^(3))dx,` (चरो को पृथक करने पर) समाकलन करने पर, `int dy =int x^(5) tan^(-1) (x^(3))dx` `impliesint dy =int x^(2). x^(3) tan ^(-1)(x^(3))dx` माना `x^(3) =t implies3x^(2) dx+dt `या ` x^(2)dx =(dt)/(3)` `therefore int dy =1/3 int underset(II)t underset(I)tan ^(-1)t dt` `impliesy=1/3 [tan ^(-1)t. (t^(2))/(2)-int(1)/(1+ t^(2)). (t^(2))/(2)dt]` `implies y=(t ^(2))/(6)tan ^(-1)t -1/6int (t^(2))/(1+t^(2))dt` `impliesy=(t^(2))/(6).tan ^(-1)t -1/6 int ((1+ t^(2)))/((1+t^(2)))dt` ` y=(t^(2))/(6)tan^(-1) t -1/6[int1 dt -int (1)/(1+t^(2))dt]` `impliesy=(t^(2))/(6) tan ^(-1) t -(1)/(6)t +1/6 tan ^(-1) t+C` `y=(x^(6))/(6) tan ^(-1) (x^(3))-(x^(3))/(6)+ 1/6 tan ^(-1) (xx^(3))+C.` |
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