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Solution of the differential equation x=1+xy^((dy)/(dx) + ((xy)^(2))/(2!) ((dy)/(dx))^(2) + ((xy)^(3))/(3!) ((dy)/(dx))^(3) +……. is |
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Answer» `y log_(e)X +C` `RARR logx = xy (dy)/(dx) rArr ydy (log x)/x dx` On INTEGRATION, we get `y^(2)2 = (log_(e)x)^(2)/2 + C` `y^(2) = (log_(e)x)^(2) + C` Hence, `y = +- sqrt((log_(e)x)^(2) + 2C)` |
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