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Differential Equations - ISC Class 12 Mathematics Questions with Answers, Page 2

50 past-paper questions on Differential Equations from ISC Class 12 Mathematics papers (2027-2017), newest first, in full. Questions 21-40 are on this page, 20 to a page. Tap "Show answer" under a question to see its answer.

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2025 · 1 mark · Assertion-reasonOpen: Degree of the differential equation cannot be determined. Assertion (A): Degree…

Assertion: Degree of the differential equation $a\left(\frac{dy}{dx}\right)^2 + b\frac{dy}{dx} = c$ cannot be determined.

Reason: If each term involving derivatives of a differential equation is a polynomial (or can be expressed as a polynomial) then the highest exponent of the highest order derivative is called the degree of the differential equation.

Assertion (A): Degree of the differential equation $a\left(\frac{dy}{dx}\right)^2 + b\frac{dy}{dx} = c$ cannot be determined. Reason (R): If each term involving derivatives of a differential equation is a polynomial (or can be expressed as a polynomial) then the highest exponent of the highest order derivative is called the degree of the differential equation.
  • (a)Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
  • (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
  • (c)Assertion (A) is true, but Reason (R) is false.
  • (d)Assertion (A) is false, but Reason (R) is true.

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2023 · 1 mark · MCQOpen: The degree of the differential equation is:
The degree of the differential equation $\frac{d^2y}{dx^2} + 3 \left(\frac{dy}{dx}\right)^2 = x^2 \log \left(\frac{d^2y}{dx^2}\right)$ is:
  • (a)$2$
  • (b)$1$
  • (c)$3$
  • (d)not defined

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2021 · 2 marks · Short answerOpen: Solve
Solve $\frac{dy}{dx} = 1 - xy + y - x$

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