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JEE Main Differential Equations questions

37 Mathematics questions on Differential Equations as asked in JEE Main, newest first. 29 come with a worked solution.

  1. Let y = y(x) be the solution of the differential equation x^3 dy + (xy - 1) dx = 0, x > 0, y (1/2 ) = 3 - e. Then y(1) is equal to

    2023

  2. Let y = y(x) be the solution of the differential equation (x^2 - 3y^2) dx + 3xy dy = 0, y(1) = 1. Then 6y^2(e) is equal to

    2023

  3. Let y = f(x) be the solution of the differential equation y(x+1)dx - x^2 dy = 0, y(1) = e. Then lim_x → 0^+ f(x) is equal to

    2023 · with solution

  4. Let y = y(x) be the solution curve of the differential equation dy/dx = y/x (1 + xy^2(1 + log_e x) ), x > 0, y(1) = 3. Then (y^2(x))/9 is equal to :

    2023

  5. Let y = y(t) be a solution of the differential equation dy/dt + α y = γ e^-β t where, α > 0, β > 0 and γ > 0. Then lim_t → ∞ y(t)

    2023 · with solution

  6. Let f be a differentiable function defined on [0, (π)/2 ] such that f(x) > 0 and f(x) + int_0^x f(t)√(1 - (log_e f(t) )^2) dt = e, forall x ∈ [0, (π)/2 ] Then (6log_e f ((π)/6 ) )^2 is equal to __________.

    2023 · with solution

  7. Let f be a differentiable function such that f(1) = 2 and f'(x) = f(x) for all x ∈ R. If h(x) = f(f(x)), then h'(1) is equal to

    2019 · with solution

  8. Given that the slope of the tangent to a curve y = y(x) at any point (x, y) is 2y/(x^2). If the curve passes through the centre of the circle x^2 + y^2 - 2x - 2y = 0, then its equation is

    2019 · with solution

  9. The general solution of the differential equation (y^2 - x^3)dx - xy dy = 0 (x ≠ 0) is (where, C is a constant of integration)

    2019

  10. The solution of the differential equation, dy/dx = (x - y)^2, when y(1) = 1, is

    2019 · with solution

  11. The curve amongst the family of curves represented by the differential equation, (x^2 - y^2)dx + 2xy dy = 0, which passes through (1, 1), is

    2019 · with solution

  12. Consider the differential equation, y^2dx + (x - 1/y )dy = 0. If value of y is 1 when x = 1, then the value of x for which y = 2, is

    2019

  13. Let y = y(x) be the solution of the differential equation, dy/dx + ytan x = 2x + x^2 tan x, x ∈ (-(π)/2, (π)/2 ), such that y(0) = 1. Then

    2019

  14. Let f:[0,1] → R be such that f(xy) = f(x) · f(y), for all x, y ∈ [0,1] and f(0) ≠ 0. If y = y(x) satisfies the differential equation, dy/dx = f(x) with y(0) = 1, then y (1/4 ) + y (3/4 ) is equal to

    2019 · with solution

  15. If y = y(x) is the solution of the differential equation dy/dx = (tan x - y)sec^2 x, x ∈ (-(π)/2, (π)/2 ), such that y(0) = 0, then y (-(π)/4 ) is equal to

    2019 · with solution

  16. If cos x dy/dx - y sin x = 6x, (0 < x < (π)/2 ) and y ((π)/3 ) = 0, then y ((π)/6 ) is equal to

    2019 · with solution

  17. The solution of the differential equation xdy/dx + 2y = x^2(x ≠ 0) with y(1) = 1, is

    2019 · with solution

  18. Let y = y(x) be the solution of the differential equation, (x^2 + 1)^2 dy/dx + 2x(x^2 + 1)y = 1 such that y(0) = 0. If √(a) y(1) = (π)/32, then the value of 'a' is

    2019 · with solution

  19. If a curve passes through the point (1, -2) and has slope of the tangent at any point (x, y) on it as (x^2 - 2y)/x, then the curve also passes through the point

    2019 · with solution

  20. Let y = y(x) be the solution of the differential equation, xdy/dx + y = xlog_e x, (x > 1). If 2y(2) = log_e 4 - 1, then y(e) is equal to

    2019 · with solution

  21. If y(x) is the solution of the differential equation dy/dx + ((2x+1)/x )y = e^-2x, x > 0, where y(1) = 1/2e^-2, then

    2019

  22. If dy/dx + 3/(cos^2 x) y = 1/(cos^2 x), x ∈ ((-π)/3, (π)/3 ) and y ((π)/4 ) = 4/3, then y (-(π)/4 ) equals

    2019 · with solution

  23. Let y = y(x) be the solution of the differential equation sin x dy/dx + ycos x = 4x, x ∈ (0, π). If y ((π)/2 ) = 0, then y ((π)/6 ) is equal to

    2018 · with solution

  24. If (2 + sin x)dy/dx + (y+1)cos x = 0 and y(0) = 1, then y ((π)/2 ) is equal to

    2017 · with solution

  25. If y = y(x) satisfies the differential equation 8√(x) (√(9+√(x)) )dy = (√(4+√(9+√(x))) )^-1dx, x > 0 and y(0) = √(7), then y(256) =

    2017 · with solution

  26. If a curve y = f(x) passes through the point (1, -1) and satisfies the differential equation, y(1 + xy)dx = x dy, then f (-1/2 ) is equal to

    2016 · with solution

  27. Let y(x) be the solution of the differential equation (x log x) dy/dx + y = 2x log x, (x ≥ 1). Then, y(e) is equal to

    2015

  28. Let the population of rabbits surviving at a time t be governed by the differential equation (dp(t))/dt = 1/2p(t) - 200. If p(0) = 100, then p(t) is equal to

    2014 · with solution

  29. The function y = f(x) is the solution of the differential equation dy/dx + xy/(x^2-1) = fracx^4+2x√(1-x^2) in (-1,1) satisfying f(0) = 0. Then int_-frac√(3)2^frac√(3)2 f(x) dx is

    2014 · with solution

  30. A curve passes through the point (1, (π)/6 ). Let the slope of the curve at each point (x, y) be y/x + sec (y/x ), x > 0. Then, the equation of the curve is

    2013 · with solution

  31. At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P with respect to additional number of workers x is given by dP/dx = 100 - 12√(x). If the firm employees 25 more…

    2013 · with solution

  32. The differential equation dy/dx = dfrac√(1-y^2)y determines a family of circles with

    2007 · with solution

  33. If x dy = y (dx + y dy), y(1) = 1 and y(x) > 0. Then, y(-3) is equal to

    2005 · with solution

  34. If y = y(x) and (2 + sin x)/(y + 1) (dy/dx ) = -cos x, y(0) = 1, then y ((π)/2 ) equals

    2004 · with solution

  35. If y(t) is a solution of (1+t)dy/dt - ty = 1 and y(0) = -1, then y(1) is equal to

    2003 · with solution

  36. A solution of the differential equation (dy/dx )^2 - xdy/dx + y = 0 is

    1999 · with solution

  37. The order of the differential equation whose general solution is given by y = (c_1 + c_2)cos(x + c_3) - c_4 e^x+c_5, where c_1, c_2, c_3, c_4, c_5 are arbitrary constants, is

    1998 · with solution

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