Find the solution of the following equations by using the fourth-order Runge-Kutta method with (Delta t=0.1) :
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Find the solution of the following equations by using the fourth-order Runge-Kutta method with \(\Delta t=0.1\) :
a. \(\dot{x}=x-1.5 e^{-0.5 t} ; x_{0}=1\)
b. \(\dot{x}=-t x^{2} ; x_{0}=1\).
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