JEE Main & Advanced Mathematics Differential Equations Question Bank

done Miscellaneous differential equations Total Questions - 7

• question_answer1)
  The solution of the differential equation \[x\frac{{{d}^{2}}y}{d{{x}^{2}}}=1\], given that \[y=1,\ \frac{dy}{dx}=0\]when \[x=1\], is
  A)
             \[y=x\log x+x+2\]                   done clear
  B)
             \[y=x\log x-x+2\] done clear
  C)
             \[y=x\log x+x\]                        done clear
  D)
             \[y=x\log x-x\] done clear
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• question_answer2)
  The solution of the differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=-\frac{1}{{{x}^{2}}}\]  is [MP PET 2003]
  A)
             \[y=\log x+{{c}_{1}}x+{{c}_{2}}\]                                       done clear
  B)
             \[y=-\log x+{{c}_{1}}x+{{c}_{2}}\] done clear
  C)
             \[y=-\frac{1}{x}+{{c}_{1}}x+{{c}_{2}}\]                           done clear
  D)
             None of these done clear
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• question_answer3)
  The solution of the differential equation \[{{\cos }^{2}}x\frac{{{d}^{2}}y}{d{{x}^{2}}}=1\] is
  A)
             \[y=\log \cos x+cx\]                 done clear
  B)
             \[y=\log \sec x+{{c}_{1}}x+{{c}_{2}}\] done clear
  C)
             \[y=\log \sec x-{{c}_{1}}x+{{c}_{2}}\]                                 done clear
  D)
             None of these done clear
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• question_answer4)
  The solution of  \[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{\sec }^{2}}x+x{{e}^{x}}\]is        [DSSE 1985]
  A)
                     \[y=\log (\sec x)+(x-2){{e}^{x}}+{{c}_{1}}x+{{c}_{2}}\] done clear
  B)
                     \[y=\log (\sec x)+(x+2){{e}^{x}}+{{c}_{1}}x+{{c}_{2}}\] done clear
  C)
             \[y=\log (\sec x)-(x+2){{e}^{x}}+{{c}_{1}}x+{{c}_{2}}\] done clear
  D)
             None of these done clear
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• question_answer5)
  If \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=0,\] then  [UPSEAT 1999]                             
  A)
             \[y=ax+b\]                               done clear
  B)
             \[{{y}^{2}}=ax+b\] done clear
  C)
             \[y=\log x\]                                done clear
  D)
   \[y={{e}^{x}}+c\] done clear
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• question_answer6)
  If \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+\sin x=0,\] then solution of the differential equation is.                                                                [Pb. CET 2001]
  A)
             \[\sin x+{{c}_{1}}x+{{c}_{2}}\] done clear
  B)
             \[\cos x+{{c}_{1}}x+{{c}_{2}}\] done clear
  C)
             \[\tan x+{{c}_{1}}x+{{c}_{2}}\]                                            done clear
  D)
             \[\log \sin x+{{c}_{1}}x+{{c}_{2}}\] done clear
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• question_answer7)
  The solution of the equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{e}^{-2x}}\] is               [AIEEE 2002]
  A)
             \[\frac{1}{4}{{e}^{-2x}}\]   done clear
  B)
             \[\frac{1}{4}{{e}^{-2x}}+cx+d\]            done clear
  C)
             \[\frac{1}{4}{{e}^{-2x}}+c{{x}^{2}}+d\]                        done clear
  D)
   \[\frac{1}{4}{{e}^{-2x}}+c+d\] done clear
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