GATE 2025 PI – Question 14
Which differential equation is linear?
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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**.