InterviewSolution
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InterviewSolution
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अवकल समीकरण `y-x(dy)/(dx)=a(y^(2)+(dy)/(dx))` को हल कीजिए। |
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Answer» `y-x(dy)/(dx)=a(y^(2)+(dy)/(dx))` `impliesy-x(dy)/(dx)=a(y^(2)+(dy)/(dx))` `implies y-x(dy)/(dx)=ay^(2)+a(dy)/(dx)` `implies(y-ay^(2))=(a+x)(dy)/(dx)` `implies(dx)/(a+x)=(1)/(y(1-ay))dy` `implies(1)/(a+x)dx=((1)/(y)+(a)/(1-ay))dy` (आंशिक भिन्नो में बदलने पर) `impliesint(1)/(a+x)dx=int((1)/(y)+(a)/(1-ay))dy+c_(1)` `implies log(a+x)=logy-log(1-ay)+logc` (जहाँ `c_(1)=logc`) `implies (a+x)=(c.y)/(1-ay)` |
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