Find the Solutions to X2 1 E2x
Transcript
| Time | Transcript |
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| 00:00 - 00:59 | hello friends question is solve the following differential equation X square minus 1 into DY by DX + 2 x y is equals to 1 upon X square + 1 and obviously Mod of is not equal to 1 year ok so we are given the differential equation as x square minus 1 into DY by DX + 2 x y is equals to 1 upon x square - 1 and modification not be equal to one become infinite and so this is already mentioned in the question ok so now I will divide both the sides by x square - 1 what I get is DY by DX + 2 x divided by x square minus 1 into Y is equals to 1 upon x square minus 1 whole |
| 01:00 - 01:59 | Kuwait not just seed and compare this equation with this since this equation this differential equation is of the form DY by DX + p y is equals to Q ok is equals to 2 x divided by x square - 1 and q is equals to 1 upon x square minus 1 whole square so whenever search form of differential equation is given Percy what will do is will find the integrating factor 22 e raised to the power of PDA equal to integral of PS2 x divided by x square - 10 x ok now for solving this is what I do is I'll put x square - 1st and differentiate |
| 02:00 - 02:59 | this both the sides will get 2 x 2 x minus zero differentiation of constant is zero is equals to DT so here I get e raised to the power integration of 2x DX is nothing but duty divided by x square - 1st June so integral of Duty by it will be welded to the power log of the ok and using the property of love this will come out to be = 20 then again put the value of x square minus one so I am getting this integrating factor as equals to x square minus one now solution forces differential equation is why into integrating factor is equals to integral of Hue into integrating factor |
| 03:00 - 03:59 | X + constancy putting the values here Suresh will become by into integrating factor is x square minus 1 is equals to integral of cube so queues one upon x square minus 1 whole square so one upon x square minus 1 whole square into integrating factor is x square - BA + C + 1 x square minus one will cancel this one x square - 10 will be left with X into why into x square minus 1 is equals to integral of x divided by x square - 1 + constancy ok now will use this integration |
| 04:00 - 04:59 | result which is deactivated by x square minus A square is equals to 1 by 2 log of x minus A + a ok send use this integration result here so we get why into x square minus 1 is equal to x minus 1 divided by X + 1 this one as one square + this constant see ya so finally this is our solution for this given differential equation this is the general solution which is buy into x square minus 1 is equals to 1 by 2 log of |
| 05:00 - 05:59 | x minus 1 divided by X + 1 + constancy thanks for watching |
Find the Solutions to X2 1 E2x
Source: https://www.doubtnut.com/question-answer/solve-the-following-differential-equation-x2-1dy-dx-2x-y1-x2-1-x-1-642509019