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Order or degree of the DE of a given family of curves

This type of question, asked 5 times: 10 May 2023 S2, 15 May 2023 S2, 14 May 2024 S2, 19 Apr 2025 S1, 25 Apr 2025 S2. All 5 questions below, oldest first.

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  1. Question 1

    10 May 2023 S2

    149
    The order of the differential equation, whose general solution is given by y=c1+c2cos⁡x+c3−c4ex+c5y = c_1 + c_2\cos x + c_3 - c_4 e^{x+c_5} where c1,c2,c3,c4c_1, c_2, c_3, c_4 and c5c_5 are arbitrary constants, is

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  2. Question 2

    15 May 2023 S2

    110
    The order of the differential equation, whose solution is y=C1+C2ex+C3ex+C4y = C_1 + C_2 e^x + C_3 e^{x+C_4}, is

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  3. Question 3

    14 May 2024 S2

    103
    The differential equation representing the family of curves y2=2c(x+c)y^2 = 2c(x + \sqrt{c}), where cc is a positive parameter, is of

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  4. Question 4

    19 Apr 2025 S1

    114
    The order and degree of differential equation of all tangent lines to the parabola x2=4yx^{2}= 4y is respectively.

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  5. Question 5

    25 Apr 2025 S2

    117
    The order of the differential equation whose general solution is given by y=(C1+C2)sin⁡(x+C3)−C4ex+C5y=\left( C_{1}+C_{2} \right)\sin\left( x+C_{3} \right)-C_{4}e^{x+C_{5}} is (where C1,C2,C3,C4,C5C_{1},C_{2},C_{3},C_{4},C_{5} are arbitrary constants)

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