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#1 Posted 7:25pm 05-03-10 DIFFERNTIAL ( TASTE UR SKILL )1) cos (x+y) dy = dx 2) [frac]x+y[frac]dy[/]dx[/frac][/]y-x[frac]dy[/]dx[/frac][/frac] = (1 + [frac]x[p]2[/p][/]y[p]2[/p][/frac]) ( ln ( x[p]2[/p]+y[p]2[/p] )) 3) [frac]dy[/]dx[/frac] = (4x + y + 1)[p]2[/p] 4) 2x[p]3[/p]y[p]3[/p] + x[p]4[/p]y[p]2[/p] [frac]dy[/]dx[/frac] = [frac]-b[p]2[/p][/]a[p]2[/p][/frac]y - [frac]b[p]2[/p][/]a[p]2[/p][/frac] x [frac]dy[/]dx[/frac] [ GUYS POST THE SOLN. FULL AS I CANNOT CONFIRM UR ANS. SINCE I DON'T HAVE THEM ]
In every loss, in every lie, in every truth that you'd deny
And each regret and each goodbye was a mistake too great to hide
And your voice was all I heard that I get what I deserve
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#2 Posted 7:34pm 05-03-10 Re: DIFFERNTIAL ( TASTE UR SKILL )For the first one...substitute x + y = t... in the third substitute 4x + y + 1 = t.. for the fourth one on observation it looks like the equation is x[p]4[/p]y[p]3[/p] = -b[p]2[/p]/a[p]2[/p] xy + c...par LHS main coefficients stidfy nahi ho rahey.. : (
Edited on 7:45pm 05-03-10 |
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#3 Posted 7:52pm 05-03-10 Re: DIFFERNTIAL ( TASTE UR SKILL )cost = dx/dy .... x + y = t diff. wrt to y dx/dy + 1 = dt/dy cost + 1 = dt/ dy.. now integrate it...write cost in terms of tant/2 cost = 1-tan[p]2[/p]t/2 / 1+tan[p]2[/p]t/2
Edited on 7:57pm 05-03-10 |
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#4 Posted 8:03pm 05-03-10 Re: DIFFERNTIAL ( TASTE UR SKILL )[im]http://www4a.wolframalpha.com/Calculate/MSP/MSP382199fc9i7hh7g204e00005abh0597icff582e?MSPStoreType=image/gif&s=18&w=229&h=36[/im] OR [im]http://www4a.wolframalpha.com/Calculate/MSP/MSP385199fc9i7hh7g204e00005h29ic2ba2h07efg?MSPStoreType=image/gif&s=18&w=207&h=36[/im] |
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#5 Posted 8:04pm 05-03-10 Re: DIFFERNTIAL ( TASTE UR SKILL )3) [frac]dt[/]dx[/frac] = t[p]2[/p] + 4. [frac]dt[/]t[p]2[/p] + 4[/frac] = dx. x = [frac]1[/]2[/frac] tan [p]-1[/p] ([frac]t[/]2[/frac]) x = [frac]1[/]2[/frac] tan [p]-1[/p] ([frac]4x + y + 1[/]2[/frac]) WAT ABT THE 2ND ONE????????
In every loss, in every lie, in every truth that you'd deny
And each regret and each goodbye was a mistake too great to hide
And your voice was all I heard that I get what I deserve
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#6 Posted 8:16pm 05-03-10 Re: DIFFERNTIAL ( TASTE UR SKILL )@ Manmay in 1 tan t/2 = t |
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#7 Posted 8:25pm 05-03-10 Re: DIFFERNTIAL ( TASTE UR SKILL )[im]http://codecogs.izyba.com/gif.latex?Q2%29%20%5C%20My%20%5C%20start...%5C%5C%20y/x%20%3Dt%20%3D%3E%20y%27%20%3D%20x.t%27+t%5C%5C%20%5C%5C%20%5Cleft%5B%201+%20t%20%5Cleft%28x.%5Cfrac%7Bdt%7D%7Bdx%7D+t%5Cright%29%5Cright%5D%20%3D%20%5Cleft%28-x.%5Cfrac%7Bdt%7D%7Bdx%7D%7D%5Cright%29%5Cleft%281+%20%5Cfrac%7B1%7D%7Bt%7D%5Cright%29%5Cleft%5B2ln%28x%29+%20ln%281+t%5E2%29%5Cright%5D[/im] Which reduces to.... [im]http://codecogs.izyba.com/gif.latex?%5Cfrac%7Bdt%7D%7Bdx%7D%5Cleft%5B%20t+%20ln%281+t%5E2%29%5E%7B1+1/t%7D%20+%20ln%28x%29%5E%7B2/t%20+2%7D%5Cright%5D%20+%20%5Cfrac%7B%281+t%5E2%29%7D%7Bx%7D%20%3D%200[/im] Now, if this can be converted to a linear one; ...can't see ny phurther....
...... Shielding the past, move on ......... Fearless, confident, gleaming, rejoicing ......... Knowing tht u can & knowing tht u will ...... Knowing tht fighting along is the only pill. |
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#8 Posted 4:13pm 06-03-10 Re: DIFFERNTIAL ( TASTE UR SKILL )i can't help it. please any one solve 2) and 4)
In every loss, in every lie, in every truth that you'd deny
And each regret and each goodbye was a mistake too great to hide
And your voice was all I heard that I get what I deserve
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#9 Posted 4:17pm 06-03-10 Re: DIFFERNTIAL ( TASTE UR SKILL )4) ANS IS.....x[p]3[/p]y[p]2[/p] - cxy = [frac]b[p]2[/p][/]a[p]2[/p][/frac] where c is constant.
In every loss, in every lie, in every truth that you'd deny
And each regret and each goodbye was a mistake too great to hide
And your voice was all I heard that I get what I deserve
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#10 Posted 8:09pm 25-03-10 Re: DIFFERNTIAL ( TASTE UR SKILL )4) Divide whole equation by x[p]2[/p]y[p]2[/p] and multiply by dx [im]http://codecogs.izyba.com/gif.latex?2xydx+x^{2}dy=-\frac{b^2}{a^2}\frac{ydx+xdy}{x^2y^2}[/im] [im]http://codecogs.izyba.com/gif.latex?yd(x^2)+x^{2}dy=-\frac{b^2}{a^2}\frac{d(xy)}{x^2y^2}[/im] [im]http://codecogs.izyba.com/gif.latex?d(x^2y)=-\frac{b^2}{a^2}\frac{d(xy)}{x^2y^2}[/im] integrate : [im] http://codecogs.izyba.com/gif.latex?x^2y=-\frac{b^2}{a^2}\left(-\frac{1}{xy}%20\right)+c[/im] [im]http://codecogs.izyba.com/gif.latex?x^2y^2-cxy=\frac{b^2}{a^2}[/im]
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#11 Posted 9:40pm 25-03-10 Re: DIFFERNTIAL ( TASTE UR SKILL )2) [im]http://codecogs.izyba.com/gif.latex?\frac{x+y\frac{dy}{dx}}{y-x\frac{dy}{dx}}=\left(1+\frac{x^2}{y^2}%20\right)ln(x^2+y^2)%20\\%20\\\frac{xdx+ydy}{ydx-xdy}=\left(1+\frac{x^2}{y^2}%20\right)ln(x^2+y^2)%20\\%20\\\frac{xdx+ydy}{\frac{ydx-xdy}{y^2}}=\left(x^2+y^2%20\right)ln(x^2+y^2)%20\\%20\\\frac{d(x^2+y^2)}{\left(x^2+y^2%20\right)ln(x^2+y^2)}=d\left(\frac{x}{y}%20\right)[/im] Now take: [im]http://codecogs.izyba.com/gif.latex?x^2+y^2=z%20\\\\and,\:%20\frac{x}{y}=t%20\\\\equn.\:%20becomes:%20\frac{dz}{zlnz}=dt%20\\\\or,\:%20ln(ln(z))=t+c%20\\\\solution:\:%20ln(ln(x^2+y^2))=\frac{x}{y}+c%20\\\\or,\:ln(x^2+y^2)=ke^{\frac{x}{y}}[/im]
Keyboard is mightier than the sword. Edited on 9:41pm 25-03-10 |
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#12 Posted 08:45am 26-03-10 Re: DIFFERNTIAL ( TASTE UR SKILL )thnks everyone
In every loss, in every lie, in every truth that you'd deny
And each regret and each goodbye was a mistake too great to hide
And your voice was all I heard that I get what I deserve
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