The degree and order of the differential equation y-x (dy/dx )³=a (y+(d²y)/(dx²) )² are respectively (A) 3, 1 (B) 2, 2 (C) 3, 2 (D) 4, 2

MathsCBSE Class 12 · Sample paper, session 2026-27 · 1 mark · MCQ

CBSE Class 12 Mathematics sample paper 2026-27: question 11

From the official CBSE sample question paper for 2026-27, section A, question 11, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q11 · 1 mark · MCQDifferential Equations

The degree and order of the differential equation $y - x (\frac{d y}{d x})^{3} = a (y + \frac{d ^{2} y}{d x ^{2}})^{2}$ are respectively

(A)3, 1
(B)2, 2
(C)3, 2
(D)4, 2

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

Open one hint at a time and try again before the next.

Hint 1

Find the highest derivative that appears.

Hint 2

Its power gives the degree.

Step-by-step solution

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The highest derivative present is $\frac{d ^{2} y}{d x ^{2}}$ , so the order is 2.
The equation is a polynomial in derivatives, and $\frac{d ^{2} y}{d x ^{2}}$ appears with highest power 2. So the degree is 2, giving (degree, order) $= (2, 2)$ .
1 mark

Answer: 2, 2; option (B)

Where the marks are

Finds order 2 and degree 2 (1 mark)

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Chapter: Differential Equations (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Differential Equations, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2026-27: every question, by section.

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CBSE Class 12 Mathematics sample paper 2026-27: question 11

Hints

Step-by-step solution

Revise the chapter

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