JEE Main & Advanced Mathematics Differential Equations Question Bank

done Exact defferential equations Total Questions - 11

• question_answer1)
  The solution of \[y\,dx-xdy+3{{x}^{2}}{{y}^{2}}{{e}^{{{x}^{3}}}}dx=0\] is
  A)
                  \[\frac{x}{y}+{{e}^{{{x}^{3}}}}=c\]          done clear
  B)
                  \[\frac{x}{y}-{{e}^{{{x}^{3}}}}=0\] done clear
  C)
                  \[\frac{-x}{y}+{{e}^{{{x}^{3}}}}=0\]        done clear
  D)
                  None of these done clear
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• question_answer2)
  If \[xdy=y\,(dx+ydy),\,y>0\] and \[y(1)=1,\] then \[y(-3)\] is equal to             [IIT Screening 2005]
  A)
                  1              done clear
  B)
                  3 done clear
  C)
                  5              done clear
  D)
                  ?1 done clear
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• question_answer3)
  The solution of \[(1+xy)y\,dx+(1-xy)x\,dy=0\] is
  A)
                  \[\frac{x}{y}+\frac{1}{xy}=k\]          done clear
  B)
                  \[\log \left( \frac{x}{y} \right)=\frac{1}{xy}+k\] done clear
  C)
                  \[\frac{x}{y}+\frac{1}{xy}=k\]          done clear
  D)
                  \[\log \left( \frac{x}{y} \right)=xy+k\] done clear
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• question_answer4)
  The solution of the differential equation, \[y\,dx+(x+{{x}^{2}}y)dy=0\] is              [AIEEE 2004]
  A)
                  \[\log y=cx\]           done clear
  B)
                  \[-\frac{1}{xy}+\log y=c\] done clear
  C)
                  \[-\frac{1}{xy}+\log y=c\]   done clear
  D)
                  \[-\frac{1}{xy}+\log y=c\] done clear
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• question_answer5)
  Solution of \[(xy\cos xy+\sin xy)dx+{{x}^{2}}\cos xy\,dy=0\] is
  A)
                  \[x\sin (xy)=k\]      done clear
  B)
                  \[xy\sin (xy)=k\] done clear
  C)
                  \[\frac{x}{y}\sin (xy)=k\]     done clear
  D)
                  \[x\sin (xy)=k\] done clear
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• question_answer6)
  The solution of \[(x-{{y}^{3}})dx+3x{{y}^{2}}dy=0\] is
  A)
                  \[\log x+\frac{x}{y}\]            done clear
  B)
                  \[\log x+\frac{{{y}^{3}}}{x}=k\] done clear
  C)
                  \[\log x-\frac{x}{{{y}^{3}}}=k\]      done clear
  D)
                  \[\log xy-{{y}^{3}}=k\] done clear
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• question_answer7)
  The solution of  \[y{{e}^{-x/y}}dx-(x{{e}^{-x/y}}+{{y}^{3}})dy=0\] is
  A)
                  \[\frac{{{y}^{2}}}{2}+{{e}^{-x/y}}=k\]     done clear
  B)
                  \[\frac{{{x}^{2}}}{2}+{{e}^{-x/y}}=k\] done clear
  C)
                  \[\frac{{{x}^{2}}}{2}+{{e}^{x/y}}=k\]      done clear
  D)
                  \[\frac{{{y}^{2}}}{2}+{{e}^{x/y}}=k\] done clear
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• question_answer8)
  The solution of the differential equation \[x\,dy+y\,dx-\sqrt{1-{{x}^{2}}{{y}^{2}}}dx=0\] is
  A)
                  \[{{\sin }^{-1}}xy=c-x\]    done clear
  B)
                  \[xy=\sin (x+c)\] done clear
  C)
                  \[\log (1-{{x}^{2}}{{y}^{2}})=x+c\]           done clear
  D)
                  \[y=x\sin x+c\] done clear
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• question_answer9)
  Solution of the differential equation, \[y\,dx-x\,dy+x{{y}^{2}}dx=0\] can be
  A)
                  \[2x+{{x}^{2}}y=\lambda y\]         done clear
  B)
                  \[2y+{{y}^{2}}x=\lambda y\] done clear
  C)
                  \[2y-{{y}^{2}}x=\lambda y\]           done clear
  D)
                  None of these done clear
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• question_answer10)
  If c is any arbitrary constant, then the general solution of the differential equation \[ydx-xdy=xy\,dx\] is given by  [J & K 2005]
  A)
                  \[y=cx\,{{e}^{-x}}\]           done clear
  B)
                  \[x=cy{{e}^{-x}}\] done clear
  C)
                  \[y+{{e}^{x}}=cx\]           done clear
  D)
                  \[y{{e}^{x}}=cx\] done clear
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• question_answer11)
  \[({{x}^{2}}+{{y}^{2}})dy=xydx\]. If \[y({{x}_{0}})=e\], \[y(1)=1\], then value of \[{{x}_{0}}=\]                                                [IIT Screening 2005]
  A)
                  \[\sqrt{3}e\]            done clear
  B)
                  \[\sqrt{{{e}^{2}}-\frac{1}{2}}\] done clear
  C)
                  \[\sqrt{\frac{{{e}^{2}}-1}{2}}\]       done clear
  D)
                  \[\sqrt{\frac{{{e}^{2}}+1}{2}}\] done clear
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