Initial Value Problem #1:

positive

Initial Value Problem #1:

Consider the following first order ODE:

	dy	3y	from t		= 1tot = 2.2withy_1_ = 1
	-----	= t² – -----	from t		= 1tot = 2.2withy_1_ = 1
(a)	dt	t
(a)	Solve with Euler’s explicit method using h=0.4 .
(b)	Solve with the midpoint method using h=0.4 .
(c)	Solve with the classical fourth-order Runge–Kutta method using h=0.4 .
The analytical solution of the ODE is			1	5	₊_t3·	. In each part, calculate the error between the true
The analytical solution of the ODE is			y =--	^§ ---	₊_t3·	. In each part, calculate the error between the true
			6	© _t3	¹