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GATE 2025 PI – Question 14

Engineering Mathematics · Differential Equations · 1 mark · Multiple choice

Which differential equation is linear?

  1. $dy/dx+2x=y^2$
  2. $x^3dy/dx+xy=x^2$
  3. $x\,d^2y/dx^2+2y\,dy/dx=0$
  4. $(dy/dx)^2+2x=y$

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Correct answer: (B) $x^3dy/dx+xy=x^2$

Explanation

An equation is linear in y when y and its derivatives occur only to first power and are not multiplied together. Option B has coefficients depending only on x: $x^3y^\prime+xy=x^2$. A squares y, C multiplies y by its derivative, and D squares the derivative. **B**.

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