LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Solving a System of Differential Equations Using Euler's Method Class Example: Using Euler's Method for System of D.E. First Three 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Second Class Example: 4th Order RungeKutta for System; First Two StepsPkkiaEc2IiQiIiIhIiI=This time I just created a vector values function f to store both right hand sides. PkkiZkc2ImYqNiVJInRHRiRJInhHRiRJInlHRiRGJDYkSSlvcGVyYXRvckdGJEkmYXJyb3dHRiRGJDckLCY5JSIiJDkmISIiLCZGLyIiJUYxRjJGJEYkRiQ=Qyc+SSN0MEc2IiIiISIiIj5JI3gwR0YlJCIiIyEiIkYnPkkjeTBHRiUkIiImRiw=PkkjSzFHNiItSSJmR0YkNiVJI3QwR0YkSSN4MEdGJEkjeTBHRiQ=PkkjSzJHNiItSSJmR0YkNiUsJkkjdDBHRiQiIiJJImhHRiQjRioiIiMsJkkjeDBHRiRGKiomRitGKiZJI0sxR0YkNiNGKkYqRiwsJkkjeTBHRiRGKiomRitGKiZGMjYjRi1GKkYsPkkjSzNHNiItSSJmR0YkNiUsJkkjdDBHRiQiIiJJImhHRiQjRioiIiMsJkkjeDBHRiRGKiomRitGKiZJI0syR0YkNiNGKkYqRiwsJkkjeTBHRiRGKiomRitGKiZGMjYjRi1GKkYsPkkjSzRHNiItSSJmR0YkNiUsJkkjdDBHRiQiIiJJImhHRiRGKiwmSSN4MEdGJEYqKiZGK0YqJkkjSzNHRiQ2I0YqRipGKiwmSSN5MEdGJEYqKiZGK0YqJkYwNiMiIiNGKkYqPkkjeDFHNiIsJkkjeDBHRiQiIiIqJkkiaEdGJEYnLComSSNLMUdGJDYjRidGJyZJI0syR0YkRi0iIiMmSSNLM0dGJEYtRjAmSSNLNEdGJEYtRidGJyNGJyIiJw==PkkjeTFHNiIsJkkjeTBHRiQiIiIqJkkiaEdGJEYnLComSSNLMUdGJDYjIiIjRicmSSNLMkdGJEYtRi4mSSNLM0dGJEYtRi4mSSNLNEdGJEYtRidGJyNGJyIiJw==PkkjdDFHNiIsJkkjdDBHRiQiIiJJImhHRiRGJw==PkkjSzFHNiItSSJmR0YkNiVJI3QxR0YkSSN4MUdGJEkjeTFHRiQ=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PkkjeTJHNiIsJkkjeTFHRiQiIiIqJkkiaEdGJEYnLComSSNLMUdGJDYjIiIjRicmSSNLMkdGJEYtRi4mSSNLM0dGJEYtRi4mSSNLNEdGJEYtRidGJyNGJyIiJw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=