InterviewSolution
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InterviewSolution
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अवकल समीकरण `(1+x^(2))(dy)/(dx)-x=2tan^(-1)x` का व्यापक मान ज्ञात कीजिए। |
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Answer» `(1+x^(2))(dy)/(dx)-x=2tan^(-1)x` `implies(dy)/(dx)=(2tan^(-1))/((1+x^(2)))+(x)/((1+x^(2)))` अब चर पृथक करने पर, `dy={(2tan^(-1)x)/((1+x^(2)))+(x)/((1+x^(2)))}dx` समाकलन करने पर `intdy=int2(tan^(-1))/((1+x^(2)))dx+int(x)/((1+x^(2)))dx` यदि `t=tan^(-1)ximplies1//(1+x^(2))dx=dt," तब "y=2inttdt+(1)/(2)int(2x)/((1+x^(2)))dx` `impliesy=t^(2)+(1)/(2)log(1+x^(2))+c` `y=(tan^(-1)x)^(2)+(1)/(2)log(1+x^(2))+c` |
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