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Differential Equations question

2003 · Shift 0 · Q87

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Mathematics
Differential Equations
2003 · Shift 0 · Q87

Differential Equations question

2003 · Shift 0 · Q87

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

The degree and order of the differential equation of the family of all parabolas whose axis is

x

-axis, are respectively.

A
$2, 3$
B
$2,1$
C
$1,2$
D
$3,2.$

View written solutionFree

Correct answer: DEGREE = 1, ORDER = 3, QUESTION/OPTIONS LIKELY CONTAIN AN ERROR SINCE (1,3) IS NOT LISTED

Write the family of parabolas whose axis is the $x$ -axis

A parabola with axis along the $x$ -axis has standard form

(y-k)^2 = 4a(x-h),

where $a,h,k$ are arbitrary constants.

So this family contains 3 arbitrary constants: $a,h,k$ .

Find the order of the differential equation

In general, eliminating $3$ arbitrary constants requires differentiating enough times, leading to a differential equation of order $3$ .

Hence, the order is

3.

Check the degree

The degree is the power of the highest order derivative after removing radicals/fractions in derivatives.

For this family, after elimination, the highest derivative appears polynomially and linearly in the final equation, so the degree is

1.

Thus, the differential equation has:

order $=3$
degree $=1$

Compare with options

The pair $(\text{degree},\text{order})$ is

(1,3).

But none of the given options is $(1,3)$ .

So the listed options appear inconsistent.

Compare with stored correct answer

Stored correct answer is C, i.e. $(1,2)$ .

This does not match the derived result $(1,3)$ .

Therefore, the stored answer seems incorrect.

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