The input x(t) and the output y(t) of a nonlinear system are related  through the following differential equation y(t) = x2dx/dt + 2x Prove that the describing function of this system can be given by √A6ω2 / 16 + 4A2 e jtan−1(A2ω/ 8)

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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The input x(t) and the output y(t) of a nonlinear system are related 
through the following differential equation
y(t) = x2dx/dt + 2x
Prove that the describing function of this system can be given by
√A6ω2 / 16 + 4A2 e jtan−1(A2ω/ 8) 

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