InterviewSolution
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InterviewSolution
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अवकल समीकरण `(1+e^(2x))dy+(1+y^(2))e^(x)dx=0` को हल कीजिये जहाँ y=1 यदि x=0 |
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Answer» `(1+e^(2x))dy+(1+y^(2))e^(x)dx=0` `implies(dy)/(1+y^(2))+(e^(x))/(1+e^(2x))dx=0` समाकलन में, `int(dy)/(1+y^(2))+int(e^(x)dx)/(1+e^(2x))=0` `impliestan^(-1)y+tan(e^(x))=c" ".......(1)` प्रश्नानुसार, जब x=0 तब y=1 `impliestan^(-1)1+tan^(-1)(e^(0))=c` `implies(pi)/(4)+(pi)/(4)=cimpliesc=(pi)/(4)` अतः समीकरण (1) से, `tan^(-1)y+tan^(-1)(e^(x))=(pi)/(2)` |
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