Out of the following systems with input x(t) and output y(t), identify the linear system.
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Answer & Explanation
Correct AnswerB. dy/dt + 2t y(t) = t²x(t)
Quick Explanation
A system is linear when input, output and output derivatives appear only to the first power and are not multiplied together; coefficients may still depend on time. In option B, dy/dt+2t y=t²x satisfies this condition. The other listed equations contain squared signal terms. Therefore option B is linear.
Formula / Key Relation
Linear form: a1(t)dy/dt+a0(t)y=b0(t)x
Detailed Explanation
Correct Answer
B — dy/dt + 2t y(t) = t²x(t)
Concept and Reasoning
A system is linear when input, output and output derivatives appear only to the first power and are not multiplied together; coefficients may still depend on time. In option B, dy/dt+2t y=t²x satisfies this condition. The other listed equations contain squared signal terms. Therefore option B is linear.
Calculation / Key Relation
Linear form: a1(t)dy/dt+a0(t)y=b0(t)x
Exam Takeaway
Time-varying coefficients do not make a system nonlinear.
Common Mistake
Look for powers/products of x, y or derivatives, not merely the presence of t-dependent coefficients.
Quick Trick
Time-varying coefficients do not make a system nonlinear.
Common Mistake
Look for powers/products of x, y or derivatives, not merely the presence of t-dependent coefficients.
Exam Tip
Time-varying coefficients do not make a system nonlinear.
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