Consider the following first-order ODE dy/dx=x^2/y from x = 0 to x = 2.4 with y(0)...

Consider the following first-order ODE dy/dx=x^2/y from x = 0 to x = 2.4 with y(0) = 2. (a) solving with Euler’s explicit method using h = 0.6 (b) solving with midpoint method using h = 0.6 (c) solving with classical fourth-order Runge-Kutta method using h = 0.6. Plot the x-y curve according to your solution for both (a) and (b).

Expert Solution

n	Xn	Yn	K1	K2
0	0	2	0	0.0270
1	0.6	2.0270	0.1066	0.2336
2	1.2	2.2606	0.3822	0.5506
3	1.8	2.8113	0.6915	0.8381
4	2.4	3.6494	0.9470	1.0609

n	Xn	Yn	K1	K2	K3	K4
0	0	2	0	0.0270	0.0268	0.1066
1	0.6	2.0357	0.106106	0.2327	0.2258	0.3820
2	1.2	2.2699	0.380634	0.5487	0.5306	0.6942
3	1.8	2.8088	0.692109	0.8387	0.8197	0.9525
4	2.4	3.6357	0.950575	1.0640	1.0495	1.1526

d)

Colby Messinger answered 3 years ago

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dy/dx + y/x \ x3y2

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