Solve the following differential equations using the given method

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Euler's Method

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1) Solve differential equation y' = 3t2y in [0,1] using Euler's method with n=10,y(0)=1.


Runge-Kutta Second Order Method (RK2)

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2) Solve differential equation y' = 2ty in [0,1] using RK2 method yn+1=yn+h/4(k1+3K2) where k1=f(tn,yn),k2=f(tn+2/3h,yn+2/3hk1)with n=5,y(0)=1.


Adams-Bashforth Two Step

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3) Solve differential equation y' = 2ty in [0,1] using Two step Adams Bashforth method with n=5,y(0)=1.


Runge-Kutta Fourth Order (RK4)

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4) Solve the ODE   on the interval  , using three steps of the Runge-Kutta 4 method with   and  .