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Match the relation for derivatives given in List II with the relation given in List I and then choose the correct code. |
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Answer» <P>`{:(a,b,c,d),(q,p,s,r):}` `"so "y^(2)+(xy-1)y_(1)=0` b. `ysqrt(1-x^(2))=sin^(-1)x` `RARR" "-(yx)/(sqrt(1-x^(2)))+y_(1)sqrt(1-x^(2))=(1)/(sqrt(1-x^(2)))` `"so "-xy+y_(1)(1-x^(2))=1` c. `y^(2)=2x-x^(2)rArr yy_(1)=1-x` `rArr" "y_(1)^(2)+yy_(2)=-1` `"so "(1-x)^(2)/(y^(2))+yy_(2)=-1` `rArr""y^(3)y_(2)=-[1+x^(2)-2x+y^(2)]=-1` d. `y=e^(sqrt(x))+e^(-sqrt(x))` `rArr" "y_(1)=(e^(sqrt(x))-e^(-sqrt(x)))/(2sqrt(x))` `rArr" "y_(1)^(2)x=(e^(sqrt(x))-e^(-sqrt(x)))^(2)=y^(2)-4` `rArr""8y_(1)y_(2)x+4y_(1)^(2)=2yy_(1)` `rArr" "4y_(2)x+2y_(1)=y` `rArr" "xy_(2)-(1)/(2)y_(1)-(1)/(4)y=0` |
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