InterviewSolution
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InterviewSolution
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Find the general solution of the differential equations `(dy)/(dx)=sin^(-1)x` |
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Answer» `(dy)/(dx)=sin^(-1)x` `implies dy=sin^(-1)x.dx` `implies intdy=int1*sin^(-1)xdx+x` `impliesy=sin^(-1)x*int1dx-int((d)/(dx)sin^(-1)x)(int1*dx)dx+c` `implies y=sin^(-1)x` `=int(x)/(sqrt(1-x^(2)))dx+c` Let `1-x^(2)=t` `implies -2x=(dt)/(dx)` `implies xdx=(-dt)/(2)` `implies y=xsin^(-1)x-int(-dt)/(2sqrt(t))+c` `impliesy=xsin^(-1)x+(1)/(2)intt^(-1//2)dt+c` `implies y=x sin^(-1)x+sqrt(t)+c` `implies y=x sin^(-1)x+sqrt(1-x^(2))+c` |
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