InterviewSolution
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InterviewSolution
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अवकल समीकरण `(x-y^(2)x)dx-y(1-x^(2))dy=0` को हल कीजिये। |
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Answer» `(x-y^(2)x)dx-y(1-x^(2))dy=0` `impliesx(1-y^(2))dx=y(1-x^(2))dx` `implies(x)/(1-x^(2))dx=((y)/(1-y^(2)))dx` `implies(xdx)/((1-x)(1+x))=(ydy)/((1-y)(1+y))` `implies(1)/(2)[(1)/(1-x)-(1)/(1+x)]dx=(1)/(2)[(1)/(1-y)-(1)/(1+y)]dy` समाकलन से `impliesint((1)/(1+x)-(1)/(1-x))dx=int((1)/(1+y)-(1)/(1-y))dy` `log(1+x)+log(1-x)=log(1+y)+log(1-y)+logc` `implieslog(1-x^(2))=log(1-y^(2))+logc` `implieslog((1-x^(2))/(1-y^(2)))=logc` `implies(1-x^(2))=c(1-y^(2))` जबकि c स्वेच्छ अचर है। |
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