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Order and degree of a given differential equation

This type of question, asked 14 times: May 2021 S1, 3 May 2023 S1, 3 May 2023 S2, 20 Apr 2025 S1, 22 Apr 2025 S1, 23 Apr 2025 S1, 11 Apr 2026 S1, 15 Apr 2026 S2, 16 Apr 2026 S2, 18 Apr 2026 S2, 20 Apr 2026 S1, 20 Apr 2026 S2, 14 May 2026 S1, 15 May 2026 S1. All 14 questions below, oldest first.

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  1. Question 1

    May 2021 S1

    121
    The order and degree of the differential equation dydx−4dydx−7x=0\sqrt{\frac{dy}{dx}} - 4\frac{dy}{dx} - 7x = 0 are

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  2. Question 2

    3 May 2023 S1

    105
    The differential equation [1+(dydx)2]⋅(d2ydx2)1/2=kx\left[1+\left(\frac{dy}{dx}\right)^2\right]\cdot\left(\frac{d^2y}{dx^2}\right)^{1/2}=kx is of

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  3. Question 3

    3 May 2023 S2

    139
    If order and degree of the differential equation (d2ydx2)5+4(d2ydx2)5⋅d3ydx3+d3ydx3=sin⁡x\left(\frac{d^{2}y}{dx^{2}}\right)^{5}+4\left(\frac{d^{2}y}{dx^{2}}\right)^{5}\cdot\frac{d^{3}y}{dx^{3}}+\frac{d^{3}y}{dx^{3}}=\sin x, are mm and nn respectively, then the value of m2+n2m^{2}+n^{2} is equal to

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  4. Question 4

    20 Apr 2025 S1

    149
    The sum of the degree and order of the differential equation d2y dx2=dy dx−55\sqrt{\frac{d^{2}y}{\text{ }dx^{2}}}=\sqrt[5]{\frac{dy}{\text{ }dx}- 5} is

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  5. Question 5

    22 Apr 2025 S1

    114
    The degree of the differential equation d2y dx2+3( dy dx)2=x2log⁡( d2y dx2)\frac{d^{2}y}{\text{ }dx^{2}}+ 3\left( \frac{\text{ }dy}{\text{ }dx} \right)^{2}=x^{2}\log\left( \frac{{\text{ }d}^{2}y}{\text{ }dx^{2}} \right) is

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  6. Question 6

    23 Apr 2025 S1

    116
    The order and degree of the differential equation dy dx−4 dy dx−7x=0\sqrt{\frac{dy}{\text{ }dx}}- 4\frac{\text{ }dy}{\text{ }dx}- 7x= 0 is respectively

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  7. Question 7

    11 Apr 2026 S1

    87
    The order and degree of the differential equation 2+(d2ydx2)3=(d3ydx3)5/2\sqrt{2 + \left(\dfrac{d^2y}{dx^2}\right)^3} = \left(\dfrac{d^3y}{dx^3}\right)^{5/2} respectively are

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  8. Question 8

    15 Apr 2026 S2

    85
    The order and degree of the differential equation 3−(d3ydx3)73=(dydx)53 - \left(\dfrac{d^3y}{dx^3}\right)^{\frac{7}{3}} = \left(\dfrac{dy}{dx}\right)^5 are respectively

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  9. Question 9

    16 Apr 2026 S2

    84
    For the differential equation d3ydx3+cos⁡(d2ydx2)=0\dfrac{d^3y}{dx^3} + \cos\left(\dfrac{d^2y}{dx^2}\right) = 0, which of the following is true ?

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  10. Question 10

    18 Apr 2026 S2

    87
    The order and degree of the differential equation 1+1(dydx)2=(d2ydx2)32\sqrt{1 + \dfrac{1}{\left(\dfrac{dy}{dx}\right)^2}} = \left(\dfrac{d^2y}{dx^2}\right)^{\frac{3}{2}} are …\ldots

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  11. Question 11

    20 Apr 2026 S1

    87
    The order and degree of the differential equation (d3ydx3)23−3d2ydx2+5dydx+4=0\left(\dfrac{d^3y}{dx^3}\right)^{\frac{2}{3}} - 3\dfrac{d^2y}{dx^2} + 5\dfrac{dy}{dx} + 4 = 0 are respectively

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  12. Question 12

    20 Apr 2026 S2

    87
    The order and degree of the differential equation 1+1(dydx)2=(d2ydx2)32\sqrt{1 + \dfrac{1}{\left(\frac{dy}{dx}\right)^2}} = \left(\dfrac{d^2y}{dx^2}\right)^{\frac{3}{2}}, respectively are

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  13. Question 13

    14 May 2026 S1

    86
    Degree of differential equation (dydx)2+53=1+(dxdy)34+(dydx)5\sqrt[3]{\left(\dfrac{dy}{dx}\right)^2 + 5} = \dfrac{1 + \left(\dfrac{dx}{dy}\right)^3}{\sqrt{4 + \left(\dfrac{dy}{dx}\right)^5}} is

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  14. Question 14

    15 May 2026 S1

    87
    The order and degree of the differential equation edydx+dydx=xe^{\frac{dy}{dx}} + \dfrac{dy}{dx} = x is

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