JEE Main & Advanced Mathematics Differential Equations Question Bank

done Numerical Value Type Questions - Differential Equations Total Questions - 15

• question_answer1)
  If \[y=y(x)\] is the solution of the differential equation, \[x\frac{dy}{dx}+2y={{x}^{2}}\] satisfying \[y(1)=1,\] then \[4y\left( \frac{1}{2} \right)\] is equal to
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• question_answer2)
  Let \[f:[0,1]\to R\] be such that \[f(xy)=f(x).f(y),\] for all \[x,y\in [0,1],\] and \[f(0)\ne 0\]. If \[y=y(x)\] satisfies the differential equation, \[\frac{dy}{dx}=f(x)\] with \[y(0)=1,\] then \[y\left( \frac{1}{4} \right)+y\left( \frac{3}{4} \right)\]is equal to
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• question_answer3)
  Let \[y=y(x)\] be the solution of the differential equation, \[x\frac{dy}{dx}+y=x\,\,{{\log }_{e}}x,\] \[(x>1).\] If \[2y(2)={{\log }_{e}}4-1,\] and \[y(e)\]is equal to \[\frac{e}{k},\] then find k.
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• question_answer4)
  The degree of the differential equation  is
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• question_answer5)
  If m and n are degree and order of \[{{\left( 1+{{y}_{1}}^{2} \right)}^{2/3}}={{y}_{2}},\] then the value of \[\frac{m+n}{m-n}\] is
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• question_answer6)
  The solution of the differential equation   satisfying \[y(0)=\frac{1}{8},\] \[y'(0)=0\] and \[y''(0)=1\] is equal to  then find the value of p.
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• question_answer7)
  A particle starts at the origin and moves along the x-axis in such a way that its velocity at the point \[(x,0)\] is given by the formula \[\frac{dx}{dt}={{\cos }^{2}}nx.\] Then the particle never reaches the point on
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• question_answer8)
  If \[y(t)\] is a solution of  and \[y(0)=-1,\] and \[y(1)\] is equal to \[\frac{-1}{k},\] then k is equal to
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• question_answer9)
  The solution of the equation  is of the form   then m is
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• question_answer10)
  Let \[y=y(x)\] be  the solution of the differential equation, \[{{({{x}^{2}}+1)}^{2}}\frac{dy}{dx}+2x({{x}^{2}}+1)y=1\] such that \[y(0)=0.\] If \[\sqrt{a}\,\,y(1)=\pi ,\] then the value of  'a'  is
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• question_answer11)
      The solution of the differential equation \[x\frac{dy}{dx}+2y={{x}^{2}}\]\[(x\ne 0)\] with \[y(1)=1,\] is of the form, \[y=\frac{{{x}^{2}}}{k}+\frac{3}{k}{{x}^{2}}.\] Then, find the value of k.
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• question_answer12)
  If \[\cos x\frac{dy}{dx}-y\sin x=6x,\]  and \[y\left( \frac{\pi }{3} \right)=0,\] If, \[y\left( \frac{\pi }{6} \right)\] is equal to  then find a.
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• question_answer13)
  If \[y=y(x)\] is the solution of the differential equation  such that \[y(0)=0,\] if  is equal to \[-k+e.\] Find k.
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• question_answer14)
  Consider the differential equation, . If value of y is 1 when \[x=1\] and the value of x for which \[y=2\] is \[k-\frac{1}{\sqrt{e}}.\]Then, find the value of k.
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• question_answer15)
  The order of the differential equation of the family of all parabolas whose axis is x-axis, is
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