Solving ODE analytically using Laplace Transform

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I want to solve the equation
(dq_Pl (t))/dt = f_(Pl,T) R_T (kN_(T,o))/(N_(T,o)+(k-N_(T,o) ) e^(-k_GR t) ) + f_(Pl,H) R_H N_(H,0)- k_El q_Pl (t)
for qPL(t), Analytically by using Laplace transform.

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