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JEE Mathematics · Medium

Calculus Mixed Practice: Differential equations MCQ

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Differential equationsMediumQuestion 430003

Question

The equation of the curve whose slope at (x,y) is 3x² and which passes through (1,2) is:
  1. A
    y = x³ + 1
    Correct
  2. B
    y = x³
  3. C
    y = 3x + 2
  4. D
    y = x³ − 1

Correct answer

y = x³ + 1

Explanation

dy/dx = 3x² → y = x³ + C. At (1,2): 2 = 1 + C → C = 1. Curve: y = x³ + 1.

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