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Let the input be $u$ and the output be $y$ of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system:

  1. $\dfrac{\mathrm{d^{3}y} }{\mathrm{d^{3}} t}+a_{1}\dfrac{\mathrm{d^{2}y} }{\mathrm{d} t^{2}}+a_{2}\dfrac{\mathrm{d} y}{\mathrm{d} t}+a_{3}y=b_{3}u+b_{2}\dfrac{\mathrm{d} u}{\mathrm{d} t}+b_{1}\dfrac{\mathrm{d^{2}}u }{\mathrm{d} t^{2}}$ (with initial rest conditions)
  2. $y\left ( t \right )=\int ^{t}_{0}e^{\alpha (t-\tau )}\beta u\left ( \tau \right )d\tau$
  3. $y=au+b,b\neq 0$
  4. $y=au$
in Differential Equations by (1.5k points)
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